(x-1)(x-1)=2x^2-x-29

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Solution for (x-1)(x-1)=2x^2-x-29 equation:


Simplifying
(x + -1)(x + -1) = 2x2 + -1x + -29

Reorder the terms:
(-1 + x)(x + -1) = 2x2 + -1x + -29

Reorder the terms:
(-1 + x)(-1 + x) = 2x2 + -1x + -29

Multiply (-1 + x) * (-1 + x)
(-1(-1 + x) + x(-1 + x)) = 2x2 + -1x + -29
((-1 * -1 + x * -1) + x(-1 + x)) = 2x2 + -1x + -29
((1 + -1x) + x(-1 + x)) = 2x2 + -1x + -29
(1 + -1x + (-1 * x + x * x)) = 2x2 + -1x + -29
(1 + -1x + (-1x + x2)) = 2x2 + -1x + -29

Combine like terms: -1x + -1x = -2x
(1 + -2x + x2) = 2x2 + -1x + -29

Reorder the terms:
1 + -2x + x2 = -29 + -1x + 2x2

Solving
1 + -2x + x2 = -29 + -1x + 2x2

Solving for variable 'x'.

Reorder the terms:
1 + 29 + -2x + x + x2 + -2x2 = -29 + -1x + 2x2 + 29 + x + -2x2

Combine like terms: 1 + 29 = 30
30 + -2x + x + x2 + -2x2 = -29 + -1x + 2x2 + 29 + x + -2x2

Combine like terms: -2x + x = -1x
30 + -1x + x2 + -2x2 = -29 + -1x + 2x2 + 29 + x + -2x2

Combine like terms: x2 + -2x2 = -1x2
30 + -1x + -1x2 = -29 + -1x + 2x2 + 29 + x + -2x2

Reorder the terms:
30 + -1x + -1x2 = -29 + 29 + -1x + x + 2x2 + -2x2

Combine like terms: -29 + 29 = 0
30 + -1x + -1x2 = 0 + -1x + x + 2x2 + -2x2
30 + -1x + -1x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
30 + -1x + -1x2 = 0 + 2x2 + -2x2
30 + -1x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
30 + -1x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(6 + x) = 0

Subproblem 1

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Subproblem 2

Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6

Solution

x = {5, -6}

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