Solve the equation?

Question

Solve for x:

(x-1)^2 =2x^2 -x -11

(If there is more than one solution, separate them with commas.)

Answer 1

(x-1)² = 2x² - x - 11
x² - 2x + 1 = 2x² - x - 11
0 = x² + x - 12
0 = (x + 4)(x - 3)
x = 3, x = -4

Answer 2

expand the equation first
x^2-2x+1=2x^2-x-11
now collect all terms to LHS
-x^2-x+12=0
(-x+3)(x+4)=0
x=3,-4
check by subbing into original equation
(3-1)^2=2(3)^2-3-11
4=4 (OK)

(-4-1)^2=2(-4)^2-(-4)-11
25=25 (OK)

therefore
x=3,-4

Answer 3

solve the left part of the equation first:
(x-1)^2 means:(x-1)(x-1)

then distribute using foil:
x^2-1x-1x+1

combine like terms:
x^2-2x+1

that is the left side of the equation; now make that equal to the orginal right side of the equation:
x^2-2x+1=2x^2-x-11

Combine like terms; subtract x^2 from 2x^2 on the right side:
-2x+1=1x^2-x-11

Combine like terms;add 11 to both sides:
-2x+12=1x^2-x

Combine like terms; add the -2x to both sides:
12=1x^2+x

subtract 12 from both sides to make the equation equal to 0:
1x^2+x-12=0

Use FOIL to solve:
(x-4)(x-3)=0

Set each equation equal to 0:
(x-4)=0 (x+3)=0

Solve both equations for X:
add 4 subtract 3

ANSWER: x=4 x= -3