Solve using the quadratic formula:?

x2 - 3x = 7x - 2
x2 - 10x - 2 = 0

x = (-b +/- sqrt (b^2 - 4ac))/2a
x = (10 +/- sqrt (100 +8))/2
x = (10 +/- sqrt(108))/2
x = (10 +/- 6 sqrt(3))/2
x = 5 +/- 3 sqrt(3)

so
x = 5 + 3 sqrt (3), 5 - 3 sqrt(3)

a little something about the other answers
answerer 1: idk where u got all that, but its def rong since
a) u didnt use quad. formula
b) u made up some terms
c) the answer has radicals
answerer 2: ur rite about that equation, but i gave an answer
answerer 3: u did absolutely nuthing
answerer 4: ur almost rite, show ur work so that i could tell u y ur rong. one obvious way ur rong is because the +/- comes before the radical, not the rational number

10 +or- (square root of 100-8) divided by 2

x2-3x=7x-2
+3x +3x

x2=10x-2
/2 /2 (divide by 2)

x=-5x (I think)

x2 - 10 x +2 = o

The general quadratic equation is

y = ax^2 + bx + c

The quadratic formula is

x = [-b +/- sqrt(b^2-4ac)] / 2a.


so you get two solutions

x1 = [-b + sqrt(b^2-4ac)] / 2a and x2 =[-b - sqrt(b^2-4ac)] / 2a.

x2 - 3x = 7x - 2

x2 - 3x - 7x = 7x -2 -7x

x2-10x = -2

x2 - 10x +2 = -2 +2 or x2 -10x + 2 = 0

A quadratic in standard form is

ax^2 +bx + c = 0

after some algebra you have the quadratic

x^2 -10x + 2 = 0

now use the quadratic formula mentioned above.

If something multiplies to be zero, then either part can be zero.

3x - 7 = 0
or
x + 2 = 0

Part 1:
3x - 7 = 0
3x = 7
x = 7/3

Part 2:
x + 2 = 0
x = -2

Answer:
x = 7/3 or x = -2

Question Number 1 : For this equation x^2 - 7*x - 1 = - 7 , 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 : First, we have to turn equation : x^2 - 7*x - 1 = - 7 , into a*x^2+b*x+c=0 form. x^2 - 7*x - 1 = - 7 , move everything in the right hand side, to the left hand side of the equation <=> x^2 - 7*x - 1 - ( - 7 ) = 0 , which is the same with <=> x^2 - 7*x - 1 + ( 7 ) =0 , now open the bracket and we get <=> x^2 - 7*x + 6 = 0 The equation x^2 - 7*x + 6 = 0 is already in a*x^2+b*x+c=0 form. In that form, we can easily derive that the value of a = 1, b = -7, c = 6. 1A. Find the roots using Quadratic Formula ! Use the formula, 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 = -7 and c = 6, we need to subtitute a,b,c in the abc formula, with thos values. Which produce x1 = (-(-7) + sqrt( (-7)^2 - 4 * (1)*(6)))/(2*1) and x2 = (-(-7) - sqrt( (-7)^2 - 4 * (1)*(6)))/(2*1) Which is the same with x1 = ( 7 + sqrt( 49-24))/(2) and x2 = ( 7 - sqrt( 49-24))/(2) Which make x1 = ( 7 + sqrt( 25))/(2) and x2 = ( 7 - sqrt( 25))/(2) So we get x1 = ( 7 + 5 )/(2) and x2 = ( 7 - 5 )/(2) So we have the answers x1 = 6 and x2 = 1 1B. Use factorization to find the root of the equation ! x^2 - 7*x + 6 = 0 ( x - 6 ) * ( x - 1 ) = 0 The answers are x1 = 6 and x2 = 1 1C. Use completing the square to find the root of the equation ! x^2 - 7*x + 6 = 0 ,divide both side with 1 Then we get x^2 - 7*x + 6 = 0 , We know that the coefficient of x is -7 We have to use the fact that ( x + q )^2 = x^2 + 2*q*x + q^2 , and assume that q = -7/2 = -3.5 So we have make the equation into x^2 - 7*x + 12.25 - 6.25 = 0 Which can be turned into ( x - 3.5 )^2 - 6.25 = 0 So we will get (( x - 3.5 ) - 2.5 ) * (( x - 3.5 ) + 2.5 ) = 0 By using the associative law we get ( x - 3.5 - 2.5 ) * ( x - 3.5 + 2.5 ) = 0 And it is the same with ( x - 6 ) * ( x - 1 ) = 0 So we got the answers as x1 = 6 and x2 = 1

x² - 10x + 2 = 0
x = [ 10 ± √ (100 - 8) ] / 2
x = [ 10 ± √ (92) ] / 2
x = [ 10 ± 2√ 23 ] / 2
x = 5 ± √ 23

Question Number 1 :
For this equation x^2 - 3*x = 7*x - 2 , answer the following questions :
A. Find the roots using Quadratic Formula !

Answer Number 1 :
First, we have to turn equation : x^2 - 3*x = 7*x - 2 , into a*x^2+b*x+c=0 form.
x^2 - 3*x = 7*x - 2 , move everything in the right hand side, to the left hand side of the equation
<=> x^2 - 3*x - ( 7*x - 2 ) = 0 , which is the same with
<=> x^2 - 3*x + ( - 7*x + 2 ) =0 , now open the bracket and we get
<=> x^2 - 10*x + 2 = 0

The equation x^2 - 10*x + 2 = 0 is already in a*x^2+b*x+c=0 form.
So we can imply that the value of a = 1, b = -10, c = 2.

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 = 2,
we just need to subtitute the value of a,b and c in the abc formula.
So x1 = (-(-10) + sqrt( (-10)^2 - 4 * (1)*(2)))/(2*1) and x2 = (-(-10) - sqrt( (-10)^2 - 4 * (1)*(2)))/(2*1)
Which is the same with x1 = ( 10 + sqrt( 100-8))/(2) and x2 = ( 10 - sqrt( 100-8))/(2)
Which make x1 = ( 10 + sqrt( 92))/(2) and x2 = ( 10 - sqrt( 92))/(2)
We can get x1 = ( 10 + 9.59166304662544 )/(2) and x2 = ( 10 - 9.59166304662544 )/(2)
So we got the answers as x1 = 9.79583152331272 and x2 = 0.204168476687281

x^2-3x-7x+2=0
x^2-10x+2=0
This equation is of form ax^2+bx+c
a = 1 b = -10 c = 2
x=[-b+/-sqrt(b^2-4ac)]/2a]
x=[10 +/-sqrt(-10^2-4(1)(2)]/(2)(1)
discriminant is b^2-4ac =92
x=[10 +√(92)] / (2)(1)
x=[10 -√(92)] / (2)(1)
x=[10+9.591663046625438] / 2
x=[10-9.591663046625438] / 2
The roots are 9.7958 and 0.2042