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Simplifying 460 = 4x2 + 38x + 88 Reorder the terms: 460 = 88 + 38x + 4x2 Solving 460 = 88 + 38x + 4x2 Solving for variable 'x'. Combine like terms: 460 + -88 = 372 372 + -38x + -4x2 = 88 + 38x + 4x2 + -88 + -38x + -4x2 Reorder the terms: 372 + -38x + -4x2 = 88 + -88 + 38x + -38x + 4x2 + -4x2 Combine like terms: 88 + -88 = 0 372 + -38x + -4x2 = 0 + 38x + -38x + 4x2 + -4x2 372 + -38x + -4x2 = 38x + -38x + 4x2 + -4x2 Combine like terms: 38x + -38x = 0 372 + -38x + -4x2 = 0 + 4x2 + -4x2 372 + -38x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 372 + -38x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(186 + -19x + -2x2) = 0 Factor a trinomial. 2((6 + -1x)(31 + 2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Subproblem 2
Set the factor '(31 + 2x)' equal to zero and attempt to solve: Simplifying 31 + 2x = 0 Solving 31 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + 2x = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 2x = 0 + -31 2x = 0 + -31 Combine like terms: 0 + -31 = -31 2x = -31 Divide each side by '2'. x = -15.5 Simplifying x = -15.5Solution
x = {6, -15.5}
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