Complete the square of: 2x^2-10x=-8?
回答 (22)
2016-06-14 10:50 pm
x² - 5x = - 4
x² - 5x + 25/4 = - 4 + 25/4
[ x - 5/2 ]² = 9/4
x - 5/2 = ± 3/2
x = 5/2 ± 3/2
x = 1 , 4
x² - 5x + 25/4 = - 4 + 25/4
[ x - 5/2 ]² = 9/4
x - 5/2 = ± 3/2
x = 5/2 ± 3/2
x = 1 , 4
2016-06-14 10:46 pm
First, you want a coefficient of 1 in front of x², so divide everything by 2:
x² - 5x = -4
Now complete the square as follows:
a. Take the coefficient in front of x --> -5
b. Halve it --> -5/2
c. Square it --> (-5/2) = 25/4
d. Add this to both sides
x² - 5x + 25/4 = -4 + 25/4
Rewrite the left side as a perfect square (refer to step b if you need help):
(x - 5/2)(x - 5/2) = -16/4 + 25/4
(x - 5/2)² = 9/4
Now take the square root of both sides; remember the ± sign:
x - 5/2 = ±√(9/4)
x - 5/2 = ± 3/2
Add 5/2 to both sides to isolate x:
x = 5/2 ± 3/2
Compute the two solutions:
x = 5/2 - 3/2 = 2/2 = 1
or
x = 5/2 + 3/2 = 8/2 = 4
Answer:
x = 1 or x = 4
P.S. It would have been much simpler to factor this.
2(x - 1)(x - 4) = 0
x² - 5x = -4
Now complete the square as follows:
a. Take the coefficient in front of x --> -5
b. Halve it --> -5/2
c. Square it --> (-5/2) = 25/4
d. Add this to both sides
x² - 5x + 25/4 = -4 + 25/4
Rewrite the left side as a perfect square (refer to step b if you need help):
(x - 5/2)(x - 5/2) = -16/4 + 25/4
(x - 5/2)² = 9/4
Now take the square root of both sides; remember the ± sign:
x - 5/2 = ±√(9/4)
x - 5/2 = ± 3/2
Add 5/2 to both sides to isolate x:
x = 5/2 ± 3/2
Compute the two solutions:
x = 5/2 - 3/2 = 2/2 = 1
or
x = 5/2 + 3/2 = 8/2 = 4
Answer:
x = 1 or x = 4
P.S. It would have been much simpler to factor this.
2(x - 1)(x - 4) = 0
2016-06-15 7:39 am
2x^2 - 10x = -8
Factoring is easier than completing the square.
2x^2 - 10x + 8 = 0
2(x^2 - 5x + 4) = 0
2(x - 1)(x - 4) = 0
Solutions:
x = 1
x = 4
Factoring is easier than completing the square.
2x^2 - 10x + 8 = 0
2(x^2 - 5x + 4) = 0
2(x - 1)(x - 4) = 0
Solutions:
x = 1
x = 4
2016-06-16 2:32 pm
the question calls for completing the square, not factoring folks
.. .. 2x² - 10x = -8
.. .. ..x² - 5x = -4
.. . .. x² - 5x + (5/2)² = -4 + (5/2)²... <=== add 1/2 of the coeff of the x term squared to both sides
.. .... (x - 5/2)² = -4 + 25/4... .. ... ....<=== factoring the left.. which is our perfect square
.. . .. (x - 5/2)² = 9/4
.. ... . x - 5/2 = ±√(9/4)
.. .. . .x = 5/2 ± 3/2
so
.. .. . . x = 8/2 = 4
.. .. . . x = 2/2 = 1
.. .. 2x² - 10x = -8
.. .. ..x² - 5x = -4
.. . .. x² - 5x + (5/2)² = -4 + (5/2)²... <=== add 1/2 of the coeff of the x term squared to both sides
.. .... (x - 5/2)² = -4 + 25/4... .. ... ....<=== factoring the left.. which is our perfect square
.. . .. (x - 5/2)² = 9/4
.. ... . x - 5/2 = ±√(9/4)
.. .. . .x = 5/2 ± 3/2
so
.. .. . . x = 8/2 = 4
.. .. . . x = 2/2 = 1
2016-06-15 6:29 am
2x^2-10x = -8,
So,
2[x^2 - 2*5x/2 +(5/2)^2] = 2*(5/2)^2 - 8,
Or,
2(x - 5/2)^2 = 25/2 - 8 = (25 - 16)/2 = 4.5
So,
2[x^2 - 2*5x/2 +(5/2)^2] = 2*(5/2)^2 - 8,
Or,
2(x - 5/2)^2 = 25/2 - 8 = (25 - 16)/2 = 4.5
2016-06-14 10:47 pm
2x^2 - 10x + 8 = 0
2(x^2 - 5x + 4) = 0
x^2 - 2 * (5/2)x + 4 = 0
(x - (5/2))^2 - (5/2)^2 + 4 = 0
(x - 5/2)^2 - 25/4 + 4 = 0
(x - 5/2)^2 = 9/4
And if you are asked to find the zeros:
x - 5/2 = ± √9/4 = ± 3/2
x = 5/2 ± 3/2
x = 2/2, 8/2
x = 1, 4
2(x^2 - 5x + 4) = 0
x^2 - 2 * (5/2)x + 4 = 0
(x - (5/2))^2 - (5/2)^2 + 4 = 0
(x - 5/2)^2 - 25/4 + 4 = 0
(x - 5/2)^2 = 9/4
And if you are asked to find the zeros:
x - 5/2 = ± √9/4 = ± 3/2
x = 5/2 ± 3/2
x = 2/2, 8/2
x = 1, 4
2016-06-16 2:14 am
X= 1, 4
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2016-06-14 10:49 pm
2x^2-10x=-8
2x^2 - 10x + 8 = 0
2(x^2 - 5x + 4) = 0
2(x - 4)(x - 1) = 0
x = 4, 1
The answer is... x = 4 or x = 1.
2x^2 - 10x + 8 = 0
2(x^2 - 5x + 4) = 0
2(x - 4)(x - 1) = 0
x = 4, 1
The answer is... x = 4 or x = 1.
2016-06-15 11:12 am
{1,4}
2016-06-15 2:53 pm
2x^2-10x+8 = 0
2(x^2-5x+4) = 0
2(x-4)(x-1) = 0
x = 4,1
2(x^2-5x+4) = 0
2(x-4)(x-1) = 0
x = 4,1
2016-07-20 8:58 am
{1,4}
2016-06-18 12:26 pm
2x^2 -10x +8=0
2(x^2 -5x +4)=0
2[(x- 2.5)^2 -6.25 +4]=0
2[(x- 2.5)^2- 2.25]=0
2(x- 2.5)^2 - 4.5
2(x^2 -5x +4)=0
2[(x- 2.5)^2 -6.25 +4]=0
2[(x- 2.5)^2- 2.25]=0
2(x- 2.5)^2 - 4.5
2016-06-18 9:08 am
2x^2 -10x = -8, ie., x^2 -5x = -4, ie., (x - 5/2)^2 = (5/2)^2 -4 = (3/2)^2 & x = (5/2) (+/-) (3/2) = 1 or 4.
So 2x^2-10x+8 = 2(x^2 -5x +4) = 2(x-1)(x-4). As Puzzling says, factoring is much simpler.
So 2x^2-10x+8 = 2(x^2 -5x +4) = 2(x-1)(x-4). As Puzzling says, factoring is much simpler.
2016-06-17 2:59 pm
X= what??
2016-06-17 12:09 pm
x= 1, x= 4
2016-06-17 9:27 am
2x^2 -10x = -8
or 2x^2 -10x + 25/2 = -8+ 25/2
or 4x^2 - 20x + 25 = -16 + 25
or (2x)^2 - 2x*2*5 +(5)^2 = 9
or(2x - 5 )^2 =3^2
or 2x- 5 = +_ 3
or 2x = 5+_ 3
or 2x = 8 or 2x = 2
x= 4 or x= 1 answer
or 2x^2 -10x + 25/2 = -8+ 25/2
or 4x^2 - 20x + 25 = -16 + 25
or (2x)^2 - 2x*2*5 +(5)^2 = 9
or(2x - 5 )^2 =3^2
or 2x- 5 = +_ 3
or 2x = 5+_ 3
or 2x = 8 or 2x = 2
x= 4 or x= 1 answer
2016-06-17 8:08 am
Since 2x^2 is not a square, factor out the 2.
x^2 - 5x = -4
Then complete the square.
(x - 2.5)^2 - 2.5^2 = -4
Combine the constants.
(x - 2.5)^2 = 2.25
Solve
x - 2.5 = +/- 1.5
x = 4 or 1
x^2 - 5x = -4
Then complete the square.
(x - 2.5)^2 - 2.5^2 = -4
Combine the constants.
(x - 2.5)^2 = 2.25
Solve
x - 2.5 = +/- 1.5
x = 4 or 1
2016-06-17 1:17 am
x² - 5x = - 4
x² - 5x + 25/4 = - 4 + 25/4
[ x - 5/2 ]² = 9/4
x - 5/2 = ± 3/2
x = 5/2 ± 3/2
x = 1 , 4
x² - 5x + 25/4 = - 4 + 25/4
[ x - 5/2 ]² = 9/4
x - 5/2 = ± 3/2
x = 5/2 ± 3/2
x = 1 , 4
2016-06-16 5:11 pm
okay since you asked to complete the square:
A vertex for of this would be:
f(x) = 2(x - 5/2)^2 -9/2
A vertex for of this would be:
f(x) = 2(x - 5/2)^2 -9/2
2016-06-16 4:06 pm
2x^2-10x+8=0
2x^2-2x-8x+8=0 (since -10x=-2x-8x)
2x(x-1)-8(x-1)=0 (taking the common terms out)
(X-1)(2x-8)=0
x-1=0; 2x-8=0
x=1 and x=4 are the roots of the equation.
2x^2-2x-8x+8=0 (since -10x=-2x-8x)
2x(x-1)-8(x-1)=0 (taking the common terms out)
(X-1)(2x-8)=0
x-1=0; 2x-8=0
x=1 and x=4 are the roots of the equation.
2016-06-16 10:40 am
x= 1 or 4
2016-06-16 9:33 am
2x²-10x=-8
(√2x-5/√2)² = -8 + 25/2 = (25-16)/2 = 9/2
√2x-5/√2 = ±3/√2
2x = 5 ±3
x = 4 or x = 1
(√2x-5/√2)² = -8 + 25/2 = (25-16)/2 = 9/2
√2x-5/√2 = ±3/√2
2x = 5 ±3
x = 4 or x = 1
2016-06-16 4:35 am
x = 4,1
2016-06-15 6:53 pm
x = [1,4]
2016-06-15 5:28 am
you can read about it here.
https://en.wikipedia.org/wiki/Completing_the_square
2*x^2-10*x=-8 -> 2*x^2-10*x+8
meaning that the above can be written as:
2*(x-5/2)^2-4.5
thereby completing the square.
https://en.wikipedia.org/wiki/Completing_the_square
2*x^2-10*x=-8 -> 2*x^2-10*x+8
meaning that the above can be written as:
2*(x-5/2)^2-4.5
thereby completing the square.
2016-06-16 1:21 pm
Ask me another question when you learn to use parentheses.
2016-06-16 9:33 am
2 x^2 - 10 x = -8 ,
2 x^2 - 10x + 8 = 0,
2 ( x2 - 5 x + 4 ) = 0 ,
so ( x2 - 5x + 4 ) = 0 , since 2 is a constant ,
therefore , x2 - 5x + 4 has to be equal to ZERO,
so , x2- 4x - x + 4 = 0 .... ( as - 4 x - 1 = 4 and -4 - 1 = -5 ) ,
simplifying , we get : x ( x-4 ) -1( x - 4 ) = 0 .
Therefore , x has to be equal to 4 or 1
2 x^2 - 10x + 8 = 0,
2 ( x2 - 5 x + 4 ) = 0 ,
so ( x2 - 5x + 4 ) = 0 , since 2 is a constant ,
therefore , x2 - 5x + 4 has to be equal to ZERO,
so , x2- 4x - x + 4 = 0 .... ( as - 4 x - 1 = 4 and -4 - 1 = -5 ) ,
simplifying , we get : x ( x-4 ) -1( x - 4 ) = 0 .
Therefore , x has to be equal to 4 or 1
2016-06-16 2:31 am
2x^2-10x=-8
Step 1: Use the zero product property, so set the right side equal to zero. So in this case, add 8 to both sides.
2x^2-10x+8=0
Step 2: ALWAYS check to see if there is a Greatest Common Factor (GCF). In this case, all the coefficient (first number in each term) is divisible by 2.
2(x^2-5x+4)=0
Step 3: Since the second term (-5x) is negative, and the last term (+4) is positive, then you know that both terms on the left are going to be both x minus something. How? Because if you add negative terms, then you get a negative, but if you multiply, then you get a positive.
2(x-?)(x-?)=0
Step 4: What adds up to make a -5, but multiplies to get +4? Find all the terms that are factors of 4. (It is either 2 and 2 or 1 and 4). Figure out which one can add up to get a -5? -1+-4=-5
2(x-1)(x-4)=0
Step 5: Divide both sides by common factor (2). The 2s on the left cancel eachother out and 0/2=0.
Step 6: Set each = to 0.
(x-1)=0. (x-4)=0
X=1. X=4
Step 7: ALWAYS CHECK WORK!!
Step 1: Use the zero product property, so set the right side equal to zero. So in this case, add 8 to both sides.
2x^2-10x+8=0
Step 2: ALWAYS check to see if there is a Greatest Common Factor (GCF). In this case, all the coefficient (first number in each term) is divisible by 2.
2(x^2-5x+4)=0
Step 3: Since the second term (-5x) is negative, and the last term (+4) is positive, then you know that both terms on the left are going to be both x minus something. How? Because if you add negative terms, then you get a negative, but if you multiply, then you get a positive.
2(x-?)(x-?)=0
Step 4: What adds up to make a -5, but multiplies to get +4? Find all the terms that are factors of 4. (It is either 2 and 2 or 1 and 4). Figure out which one can add up to get a -5? -1+-4=-5
2(x-1)(x-4)=0
Step 5: Divide both sides by common factor (2). The 2s on the left cancel eachother out and 0/2=0.
Step 6: Set each = to 0.
(x-1)=0. (x-4)=0
X=1. X=4
Step 7: ALWAYS CHECK WORK!!
2016-06-15 7:53 pm
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