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Simplifying 1x2 + -8x + 1x2 + 10x = 180 Reorder the terms: -8x + 10x + 1x2 + 1x2 = 180 Combine like terms: -8x + 10x = 2x 2x + 1x2 + 1x2 = 180 Combine like terms: 1x2 + 1x2 = 2x2 2x + 2x2 = 180 Solving 2x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 2x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + x + x2) = 0 Factor a trinomial. 2((-10 + -1x)(9 + -1x)) = 0 Ignore the factor 2.Subproblem 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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-10, 9}
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