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Simplifying 180 = x2 + 100 + -2x Reorder the terms: 180 = 100 + -2x + x2 Solving 180 = 100 + -2x + x2 Solving for variable 'x'. Combine like terms: 180 + -100 = 80 80 + 2x + -1x2 = 100 + -2x + x2 + -100 + 2x + -1x2 Reorder the terms: 80 + 2x + -1x2 = 100 + -100 + -2x + 2x + x2 + -1x2 Combine like terms: 100 + -100 = 0 80 + 2x + -1x2 = 0 + -2x + 2x + x2 + -1x2 80 + 2x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 80 + 2x + -1x2 = 0 + x2 + -1x2 80 + 2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 80 + 2x + -1x2 = 0 Factor a trinomial. (10 + -1x)(8 + x) = 0Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Solution
x = {10, -8}
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