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Simplifying 4x2 + -60 = 5x2 + 17x Reorder the terms: -60 + 4x2 = 5x2 + 17x Reorder the terms: -60 + 4x2 = 17x + 5x2 Solving -60 + 4x2 = 17x + 5x2 Solving for variable 'x'. Reorder the terms: -60 + -17x + 4x2 + -5x2 = 17x + 5x2 + -17x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -60 + -17x + -1x2 = 17x + 5x2 + -17x + -5x2 Reorder the terms: -60 + -17x + -1x2 = 17x + -17x + 5x2 + -5x2 Combine like terms: 17x + -17x = 0 -60 + -17x + -1x2 = 0 + 5x2 + -5x2 -60 + -17x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -60 + -17x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(60 + 17x + x2) = 0 Factor a trinomial. -1((12 + x)(5 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Simplifying x = -12Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {-12, -5}
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