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Simplifying 9x2 + 69x = -90 Reorder the terms: 69x + 9x2 = -90 Solving 69x + 9x2 = -90 Solving for variable 'x'. Reorder the terms: 90 + 69x + 9x2 = -90 + 90 Combine like terms: -90 + 90 = 0 90 + 69x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(30 + 23x + 3x2) = 0 Factor a trinomial. 3((6 + x)(5 + 3x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 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 = {-6, -1.666666667}
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