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Simplifying 4x2 + 64x + 220 = 540 Reorder the terms: 220 + 64x + 4x2 = 540 Solving 220 + 64x + 4x2 = 540 Solving for variable 'x'. Reorder the terms: 220 + -540 + 64x + 4x2 = 540 + -540 Combine like terms: 220 + -540 = -320 -320 + 64x + 4x2 = 540 + -540 Combine like terms: 540 + -540 = 0 -320 + 64x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-80 + 16x + x2) = 0 Factor a trinomial. 4((-20 + -1x)(4 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve: Simplifying -20 + -1x = 0 Solving -20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + -1x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -1x = 0 + 20 -1x = 0 + 20 Combine like terms: 0 + 20 = 20 -1x = 20 Divide each side by '-1'. x = -20 Simplifying x = -20Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-20, 4}
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