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Simplifying 4x2 + -52 = 5x2 + 17x Reorder the terms: -52 + 4x2 = 5x2 + 17x Reorder the terms: -52 + 4x2 = 17x + 5x2 Solving -52 + 4x2 = 17x + 5x2 Solving for variable 'x'. Reorder the terms: -52 + -17x + 4x2 + -5x2 = 17x + 5x2 + -17x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -52 + -17x + -1x2 = 17x + 5x2 + -17x + -5x2 Reorder the terms: -52 + -17x + -1x2 = 17x + -17x + 5x2 + -5x2 Combine like terms: 17x + -17x = 0 -52 + -17x + -1x2 = 0 + 5x2 + -5x2 -52 + -17x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -52 + -17x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(52 + 17x + x2) = 0 Factor a trinomial. -1((13 + x)(4 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + x)' equal to zero and attempt to solve: Simplifying 13 + x = 0 Solving 13 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + x = 0 + -13 x = 0 + -13 Combine like terms: 0 + -13 = -13 x = -13 Simplifying x = -13Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {-13, -4}
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