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Simplifying 4x2 + -140 = 5x2 + 27x Reorder the terms: -140 + 4x2 = 5x2 + 27x Reorder the terms: -140 + 4x2 = 27x + 5x2 Solving -140 + 4x2 = 27x + 5x2 Solving for variable 'x'. Reorder the terms: -140 + -27x + 4x2 + -5x2 = 27x + 5x2 + -27x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -140 + -27x + -1x2 = 27x + 5x2 + -27x + -5x2 Reorder the terms: -140 + -27x + -1x2 = 27x + -27x + 5x2 + -5x2 Combine like terms: 27x + -27x = 0 -140 + -27x + -1x2 = 0 + 5x2 + -5x2 -140 + -27x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -140 + -27x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(140 + 27x + x2) = 0 Factor a trinomial. -1((20 + x)(7 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(20 + x)' equal to zero and attempt to solve: Simplifying 20 + x = 0 Solving 20 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + x = 0 + -20 x = 0 + -20 Combine like terms: 0 + -20 = -20 x = -20 Simplifying x = -20Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Solution
x = {-20, -7}
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