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Simplifying 4x2 + -42 = 5x2 + 17x Reorder the terms: -42 + 4x2 = 5x2 + 17x Reorder the terms: -42 + 4x2 = 17x + 5x2 Solving -42 + 4x2 = 17x + 5x2 Solving for variable 'x'. Reorder the terms: -42 + -17x + 4x2 + -5x2 = 17x + 5x2 + -17x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -42 + -17x + -1x2 = 17x + 5x2 + -17x + -5x2 Reorder the terms: -42 + -17x + -1x2 = 17x + -17x + 5x2 + -5x2 Combine like terms: 17x + -17x = 0 -42 + -17x + -1x2 = 0 + 5x2 + -5x2 -42 + -17x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -42 + -17x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(42 + 17x + x2) = 0 Factor a trinomial. -1((14 + x)(3 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(14 + x)' equal to zero and attempt to solve: Simplifying 14 + x = 0 Solving 14 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + x = 0 + -14 x = 0 + -14 Combine like terms: 0 + -14 = -14 x = -14 Simplifying x = -14Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {-14, -3}
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