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Simplifying 4x2 + -128 = 5x2 + 24x Reorder the terms: -128 + 4x2 = 5x2 + 24x Reorder the terms: -128 + 4x2 = 24x + 5x2 Solving -128 + 4x2 = 24x + 5x2 Solving for variable 'x'. Reorder the terms: -128 + -24x + 4x2 + -5x2 = 24x + 5x2 + -24x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -128 + -24x + -1x2 = 24x + 5x2 + -24x + -5x2 Reorder the terms: -128 + -24x + -1x2 = 24x + -24x + 5x2 + -5x2 Combine like terms: 24x + -24x = 0 -128 + -24x + -1x2 = 0 + 5x2 + -5x2 -128 + -24x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -128 + -24x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(128 + 24x + x2) = 0 Factor a trinomial. -1((16 + x)(8 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16 + x)' equal to zero and attempt to solve: Simplifying 16 + x = 0 Solving 16 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 0 + -16 Combine like terms: 16 + -16 = 0 0 + x = 0 + -16 x = 0 + -16 Combine like terms: 0 + -16 = -16 x = -16 Simplifying x = -16Subproblem 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 = {-16, -8}
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