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Simplifying 0 = 36x2 + 120x + 100 Reorder the terms: 0 = 100 + 120x + 36x2 Solving 0 = 100 + 120x + 36x2 Solving for variable 'x'. Combine like terms: 0 + -100 = -100 -100 + -120x + -36x2 = 100 + 120x + 36x2 + -100 + -120x + -36x2 Reorder the terms: -100 + -120x + -36x2 = 100 + -100 + 120x + -120x + 36x2 + -36x2 Combine like terms: 100 + -100 = 0 -100 + -120x + -36x2 = 0 + 120x + -120x + 36x2 + -36x2 -100 + -120x + -36x2 = 120x + -120x + 36x2 + -36x2 Combine like terms: 120x + -120x = 0 -100 + -120x + -36x2 = 0 + 36x2 + -36x2 -100 + -120x + -36x2 = 36x2 + -36x2 Combine like terms: 36x2 + -36x2 = 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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