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Simplifying 224 + -60x + 4x2 = 80 Solving 224 + -60x + 4x2 = 80 Solving for variable 'x'. Reorder the terms: 224 + -80 + -60x + 4x2 = 80 + -80 Combine like terms: 224 + -80 = 144 144 + -60x + 4x2 = 80 + -80 Combine like terms: 80 + -80 = 0 144 + -60x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(36 + -15x + x2) = 0 Factor a trinomial. 4((3 + -1x)(12 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Solution
x = {3, 12}
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