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Simplifying 4x2 + -152 = 5x2 + 27x Reorder the terms: -152 + 4x2 = 5x2 + 27x Reorder the terms: -152 + 4x2 = 27x + 5x2 Solving -152 + 4x2 = 27x + 5x2 Solving for variable 'x'. Reorder the terms: -152 + -27x + 4x2 + -5x2 = 27x + 5x2 + -27x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -152 + -27x + -1x2 = 27x + 5x2 + -27x + -5x2 Reorder the terms: -152 + -27x + -1x2 = 27x + -27x + 5x2 + -5x2 Combine like terms: 27x + -27x = 0 -152 + -27x + -1x2 = 0 + 5x2 + -5x2 -152 + -27x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -152 + -27x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(152 + 27x + x2) = 0 Factor a trinomial. -1((19 + x)(8 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(19 + x)' equal to zero and attempt to solve: Simplifying 19 + x = 0 Solving 19 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + x = 0 + -19 x = 0 + -19 Combine like terms: 0 + -19 = -19 x = -19 Simplifying x = -19Subproblem 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 = {-19, -8}
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