0=132-x-x^2

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Solution for 0=132-x-x^2 equation:


Simplifying
0 = 132 + -1x + -1x2

Solving
0 = 132 + -1x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -132 = -132
-132 + x + x2 = 132 + -1x + -1x2 + -132 + x + x2

Reorder the terms:
-132 + x + x2 = 132 + -132 + -1x + x + -1x2 + x2

Combine like terms: 132 + -132 = 0
-132 + x + x2 = 0 + -1x + x + -1x2 + x2
-132 + x + x2 = -1x + x + -1x2 + x2

Combine like terms: -1x + x = 0
-132 + x + x2 = 0 + -1x2 + x2
-132 + x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-132 + x + x2 = 0

Factor a trinomial.
(-12 + -1x)(11 + -1x) = 0

Subproblem 1

Set the factor '(-12 + -1x)' equal to zero and attempt to solve: Simplifying -12 + -1x = 0 Solving -12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1x = 0 + 12 -1x = 0 + 12 Combine like terms: 0 + 12 = 12 -1x = 12 Divide each side by '-1'. x = -12 Simplifying x = -12

Subproblem 2

Set the factor '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Divide each side by '-1'. x = 11 Simplifying x = 11

Solution

x = {-12, 11}

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