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Simplifying 24x2 + -4x2 + -108x + -224 = 0 Reorder the terms: -224 + -108x + 24x2 + -4x2 = 0 Combine like terms: 24x2 + -4x2 = 20x2 -224 + -108x + 20x2 = 0 Solving -224 + -108x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-56 + -27x + 5x2) = 0 Factor a trinomial. 4((-8 + -5x)(7 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-8 + -5x)' equal to zero and attempt to solve: Simplifying -8 + -5x = 0 Solving -8 + -5x = 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 + -5x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -5x = 0 + 8 -5x = 0 + 8 Combine like terms: 0 + 8 = 8 -5x = 8 Divide each side by '-5'. x = -1.6 Simplifying x = -1.6Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-1.6, 7}
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