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Simplifying 4x2 + 52x = 120 Reorder the terms: 52x + 4x2 = 120 Solving 52x + 4x2 = 120 Solving for variable 'x'. Reorder the terms: -120 + 52x + 4x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 52x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-30 + 13x + x2) = 0 Factor a trinomial. 4((-15 + -1x)(2 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-15, 2}
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