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Simplifying 0 = 24x2 + -108x + -672 Reorder the terms: 0 = -672 + -108x + 24x2 Solving 0 = -672 + -108x + 24x2 Solving for variable 'x'. Combine like terms: 0 + 672 = 672 672 + 108x + -24x2 = -672 + -108x + 24x2 + 672 + 108x + -24x2 Reorder the terms: 672 + 108x + -24x2 = -672 + 672 + -108x + 108x + 24x2 + -24x2 Combine like terms: -672 + 672 = 0 672 + 108x + -24x2 = 0 + -108x + 108x + 24x2 + -24x2 672 + 108x + -24x2 = -108x + 108x + 24x2 + -24x2 Combine like terms: -108x + 108x = 0 672 + 108x + -24x2 = 0 + 24x2 + -24x2 672 + 108x + -24x2 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 672 + 108x + -24x2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(56 + 9x + -2x2) = 0 Factor a trinomial. 12((8 + -1x)(7 + 2x)) = 0 Ignore the factor 12.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 '(7 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 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 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Divide each side by '2'. x = -3.5 Simplifying x = -3.5Solution
x = {8, -3.5}
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