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Simplifying 0 = 27x2 + 90x + 75 Reorder the terms: 0 = 75 + 90x + 27x2 Solving 0 = 75 + 90x + 27x2 Solving for variable 'x'. Combine like terms: 0 + -75 = -75 -75 + -90x + -27x2 = 75 + 90x + 27x2 + -75 + -90x + -27x2 Reorder the terms: -75 + -90x + -27x2 = 75 + -75 + 90x + -90x + 27x2 + -27x2 Combine like terms: 75 + -75 = 0 -75 + -90x + -27x2 = 0 + 90x + -90x + 27x2 + -27x2 -75 + -90x + -27x2 = 90x + -90x + 27x2 + -27x2 Combine like terms: 90x + -90x = 0 -75 + -90x + -27x2 = 0 + 27x2 + -27x2 -75 + -90x + -27x2 = 27x2 + -27x2 Combine like terms: 27x2 + -27x2 = 0 -75 + -90x + -27x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(25 + 30x + 9x2) = 0 Factor a trinomial. -3((5 + 3x)(5 + 3x)) = 0 Ignore the factor -3.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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