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Simplifying 480 = 4x2 + 24x + 32 Reorder the terms: 480 = 32 + 24x + 4x2 Solving 480 = 32 + 24x + 4x2 Solving for variable 'x'. Combine like terms: 480 + -32 = 448 448 + -24x + -4x2 = 32 + 24x + 4x2 + -32 + -24x + -4x2 Reorder the terms: 448 + -24x + -4x2 = 32 + -32 + 24x + -24x + 4x2 + -4x2 Combine like terms: 32 + -32 = 0 448 + -24x + -4x2 = 0 + 24x + -24x + 4x2 + -4x2 448 + -24x + -4x2 = 24x + -24x + 4x2 + -4x2 Combine like terms: 24x + -24x = 0 448 + -24x + -4x2 = 0 + 4x2 + -4x2 448 + -24x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 448 + -24x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(112 + -6x + -1x2) = 0 Factor a trinomial. 4((8 + -1x)(14 + x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Subproblem 2
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 = -14Solution
x = {8, -14}
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