What is x: x^2 - 10x + 25 = 0?

x^2 - 10x + 25 = 0

Factor: Find two factors of 25 that sum to -10

Those factors are -5 and -5 since -5*-5 = 25 and -5 + -5 = -10

(x - 5)(x - 5) = 0

x = 5 (double root)

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Check solution:

x^2 - 10x + 25 = 0

5^2 - 10*(5) + 25 = 0

25 - 50 + 25 = 0

-25 + 25 = 0

0 = 0 (TRUE)

for any x^2 equation, or quadratic equation, there are consistently 2 suggestions. however, consequently the two suggestions are the comparable. ( -5) so there is one distinctive value of x. answer is a million

Question Number 1 :
For this equation x^2 - 10*x + 25 = 0 , answer the following questions :
A. Find the roots using Quadratic Formula !
B. Use factorization to find the root of the equation !
C. Use completing the square to find the root of the equation !

Answer Number 1 :
The equation x^2 - 10*x + 25 = 0 is already in a*x^2+b*x+c=0 form.
By matching the constant position, we can derive that the value of a = 1, b = -10, c = 25.

1A. Find the roots using Quadratic Formula !
By using abc formula the value of x is both
x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a)
We had know that a = 1, b = -10 and c = 25,
we just need to subtitute the value of a,b and c in the abc formula.
So x1 = (-(-10) + sqrt( (-10)^2 - 4 * (1)*(25)))/(2*1) and x2 = (-(-10) - sqrt( (-10)^2 - 4 * (1)*(25)))/(2*1)
Which can be turned into x1 = ( 10 + sqrt( 100-100))/(2) and x2 = ( 10 - sqrt( 100-100))/(2)
Which is the same with x1 = ( 10 + sqrt( 0))/(2) and x2 = ( 10 - sqrt( 0))/(2)
It imply that x1 = ( 10 + 0 )/(2) and x2 = ( 10 - 0 )/(2)
So we have the answers x1 = 5 and x2 = 5

1B. Use factorization to find the root of the equation !
x^2 - 10*x + 25 = 0
( x - 5 ) * ( x - 5 ) = 0
We get following answers x1 = 5 and x2 = 5

1C. Use completing the square to find the root of the equation !
x^2 - 10*x + 25 = 0 ,divide both side with 1
Which result in x^2 - 10*x + 25 = 0 ,
We know that the coefficient of x is -10
We have to use the fact that ( x + q )^2 = x^2 + 2*q*x + q^2 , and assume that q = -10/2 = -5
So we have make the equation into x^2 - 10*x + 25 + 0 = 0
Which is the same with ( x - 5 )^2 + 0 = 0
So we will get (( x - 5 ) - 0 ) * (( x - 5 ) + 0 ) = 0
By opening the brackets we will get ( x - 5 - 0 ) * ( x - 5 + 0 ) = 0
Do the addition/subtraction, and we get ( x - 5 ) * ( x - 5 ) = 0
So we have the answers x1 = 5 and x2 = 5

(x - 5)(x - 5) = 0
x = 5

x^2 - 10x + 25 = 0
x^2 - 5x - 5x + 25 = 0
(x^2 - 5x) - (5x - 25) = 0
x(x - 5) - 5(x - 5) = 0
(x - 5)(x - 5) = 0

x - 5 = 0
x = 5

∴ x = 5

this factors to

(x-5)(x-5)=0
x=5

1) Original equation: x^2 - 10x + 25 = 0

2) Factor the perfect square: (x - 5)(x - 5) = 0

3) The two terms (x - 5) are being multiplied together where the product equals zero, therefore, at least one of the parenthesis must be equal to zero. Since the two terms are the same you only have to solve for one of them.

4) x - 5 = 0

5) Add five to each side of the equation and volia! Your answer is....

6) Answer: x = 5

okay well what you have is

x^2 - 10x + 25 = 0

youre gonna have to simplify:

(x-5) (x-5) = 0


x - 5 = 0 x - 5 = 0
+ 5 +5 + 5 + 5
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x = 5 x= 5

x^2 - 10x + 25 = 0 factors to:

(x - 5) (x - 5) = 0 then set each equal to 0,

x - 5 = 0 and x - 5 = 0 then add 5 to each side,

x = 5 is the answer

(x-5)^2 = 0
x = 5