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Simplifying 36x2 = 120x + -100 Reorder the terms: 36x2 = -100 + 120x Solving 36x2 = -100 + 120x Solving for variable 'x'. Reorder the terms: 100 + -120x + 36x2 = -100 + 120x + 100 + -120x Reorder the terms: 100 + -120x + 36x2 = -100 + 100 + 120x + -120x Combine like terms: -100 + 100 = 0 100 + -120x + 36x2 = 0 + 120x + -120x 100 + -120x + 36x2 = 120x + -120x Combine like terms: 120x + -120x = 0 100 + -120x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(25 + -30x + 9x2) = 0 Factor a trinomial. 4((5 + -3x)(5 + -3x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667Solution
x = {1.666666667, 1.666666667}
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