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Simplifying 4x2 + -170 = 5x2 + 27x Reorder the terms: -170 + 4x2 = 5x2 + 27x Reorder the terms: -170 + 4x2 = 27x + 5x2 Solving -170 + 4x2 = 27x + 5x2 Solving for variable 'x'. Reorder the terms: -170 + -27x + 4x2 + -5x2 = 27x + 5x2 + -27x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -170 + -27x + -1x2 = 27x + 5x2 + -27x + -5x2 Reorder the terms: -170 + -27x + -1x2 = 27x + -27x + 5x2 + -5x2 Combine like terms: 27x + -27x = 0 -170 + -27x + -1x2 = 0 + 5x2 + -5x2 -170 + -27x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -170 + -27x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(170 + 27x + x2) = 0 Factor a trinomial. -1((17 + x)(10 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(17 + x)' equal to zero and attempt to solve: Simplifying 17 + x = 0 Solving 17 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + x = 0 + -17 x = 0 + -17 Combine like terms: 0 + -17 = -17 x = -17 Simplifying x = -17Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10Solution
x = {-17, -10}
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