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Simplifying (4x2 + -10) + (x2 + 2x + 10) + (8x + 5) = 180 Reorder the terms: (-10 + 4x2) + (x2 + 2x + 10) + (8x + 5) = 180 Remove parenthesis around (-10 + 4x2) -10 + 4x2 + (x2 + 2x + 10) + (8x + 5) = 180 Reorder the terms: -10 + 4x2 + (10 + 2x + x2) + (8x + 5) = 180 Remove parenthesis around (10 + 2x + x2) -10 + 4x2 + 10 + 2x + x2 + (8x + 5) = 180 Reorder the terms: -10 + 4x2 + 10 + 2x + x2 + (5 + 8x) = 180 Remove parenthesis around (5 + 8x) -10 + 4x2 + 10 + 2x + x2 + 5 + 8x = 180 Reorder the terms: -10 + 10 + 5 + 2x + 8x + 4x2 + x2 = 180 Combine like terms: -10 + 10 = 0 0 + 5 + 2x + 8x + 4x2 + x2 = 180 5 + 2x + 8x + 4x2 + x2 = 180 Combine like terms: 2x + 8x = 10x 5 + 10x + 4x2 + x2 = 180 Combine like terms: 4x2 + x2 = 5x2 5 + 10x + 5x2 = 180 Solving 5 + 10x + 5x2 = 180 Solving for variable 'x'. Reorder the terms: 5 + -180 + 10x + 5x2 = 180 + -180 Combine like terms: 5 + -180 = -175 -175 + 10x + 5x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -175 + 10x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-35 + 2x + x2) = 0 Factor a trinomial. 5((-7 + -1x)(5 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7Subproblem 2
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 = 5Solution
x = {-7, 5}
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