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Simplifying 9x2 + 39x + 10 = 40 Reorder the terms: 10 + 39x + 9x2 = 40 Solving 10 + 39x + 9x2 = 40 Solving for variable 'x'. Reorder the terms: 10 + -40 + 39x + 9x2 = 40 + -40 Combine like terms: 10 + -40 = -30 -30 + 39x + 9x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -30 + 39x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + 13x + 3x2) = 0 Factor a trinomial. 3((-5 + -1x)(2 + -3x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 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 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-5, 0.6666666667}
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