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Simplifying 0 = 24x2 + 52x + 24 Reorder the terms: 0 = 24 + 52x + 24x2 Solving 0 = 24 + 52x + 24x2 Solving for variable 'x'. Combine like terms: 0 + -24 = -24 -24 + -52x + -24x2 = 24 + 52x + 24x2 + -24 + -52x + -24x2 Reorder the terms: -24 + -52x + -24x2 = 24 + -24 + 52x + -52x + 24x2 + -24x2 Combine like terms: 24 + -24 = 0 -24 + -52x + -24x2 = 0 + 52x + -52x + 24x2 + -24x2 -24 + -52x + -24x2 = 52x + -52x + 24x2 + -24x2 Combine like terms: 52x + -52x = 0 -24 + -52x + -24x2 = 0 + 24x2 + -24x2 -24 + -52x + -24x2 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 -24 + -52x + -24x2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(6 + 13x + 6x2) = 0 Factor a trinomial. -4((3 + 2x)(2 + 3x)) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 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 = {-1.5, -0.6666666667}
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