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Simplifying 4x2 + -180 = 5x2 + 28x Reorder the terms: -180 + 4x2 = 5x2 + 28x Reorder the terms: -180 + 4x2 = 28x + 5x2 Solving -180 + 4x2 = 28x + 5x2 Solving for variable 'x'. Reorder the terms: -180 + -28x + 4x2 + -5x2 = 28x + 5x2 + -28x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -180 + -28x + -1x2 = 28x + 5x2 + -28x + -5x2 Reorder the terms: -180 + -28x + -1x2 = 28x + -28x + 5x2 + -5x2 Combine like terms: 28x + -28x = 0 -180 + -28x + -1x2 = 0 + 5x2 + -5x2 -180 + -28x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -180 + -28x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(180 + 28x + x2) = 0 Factor a trinomial. -1((18 + x)(10 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(18 + x)' equal to zero and attempt to solve: Simplifying 18 + x = 0 Solving 18 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 0 + -18 Combine like terms: 18 + -18 = 0 0 + x = 0 + -18 x = 0 + -18 Combine like terms: 0 + -18 = -18 x = -18 Simplifying x = -18Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 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 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10Solution
x = {-18, -10}
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