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Simplifying 2x(2x + 13) = 48 Reorder the terms: 2x(13 + 2x) = 48 (13 * 2x + 2x * 2x) = 48 (26x + 4x2) = 48 Solving 26x + 4x2 = 48 Solving for variable 'x'. Reorder the terms: -48 + 26x + 4x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + 26x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + 13x + 2x2) = 0 Factor a trinomial. 2((-8 + -1x)(3 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Divide each side by '-1'. x = -8 Simplifying x = -8Subproblem 2
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 = 1.5Solution
x = {-8, 1.5}
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