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Simplifying 0 = 4x2 + 107x + 639 Reorder the terms: 0 = 639 + 107x + 4x2 Solving 0 = 639 + 107x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -639 = -639 -639 + -107x + -4x2 = 639 + 107x + 4x2 + -639 + -107x + -4x2 Reorder the terms: -639 + -107x + -4x2 = 639 + -639 + 107x + -107x + 4x2 + -4x2 Combine like terms: 639 + -639 = 0 -639 + -107x + -4x2 = 0 + 107x + -107x + 4x2 + -4x2 -639 + -107x + -4x2 = 107x + -107x + 4x2 + -4x2 Combine like terms: 107x + -107x = 0 -639 + -107x + -4x2 = 0 + 4x2 + -4x2 -639 + -107x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -639 + -107x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(639 + 107x + 4x2) = 0 Factor a trinomial. -1((71 + 4x)(9 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(71 + 4x)' equal to zero and attempt to solve: Simplifying 71 + 4x = 0 Solving 71 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-71' to each side of the equation. 71 + -71 + 4x = 0 + -71 Combine like terms: 71 + -71 = 0 0 + 4x = 0 + -71 4x = 0 + -71 Combine like terms: 0 + -71 = -71 4x = -71 Divide each side by '4'. x = -17.75 Simplifying x = -17.75Subproblem 2
Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Solution
x = {-17.75, -9}
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