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Simplifying (2x + 4)(2x + 5) = 306 Reorder the terms: (4 + 2x)(2x + 5) = 306 Reorder the terms: (4 + 2x)(5 + 2x) = 306 Multiply (4 + 2x) * (5 + 2x) (4(5 + 2x) + 2x * (5 + 2x)) = 306 ((5 * 4 + 2x * 4) + 2x * (5 + 2x)) = 306 ((20 + 8x) + 2x * (5 + 2x)) = 306 (20 + 8x + (5 * 2x + 2x * 2x)) = 306 (20 + 8x + (10x + 4x2)) = 306 Combine like terms: 8x + 10x = 18x (20 + 18x + 4x2) = 306 Solving 20 + 18x + 4x2 = 306 Solving for variable 'x'. Reorder the terms: 20 + -306 + 18x + 4x2 = 306 + -306 Combine like terms: 20 + -306 = -286 -286 + 18x + 4x2 = 306 + -306 Combine like terms: 306 + -306 = 0 -286 + 18x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-143 + 9x + 2x2) = 0 Factor a trinomial. 2((-11 + -1x)(13 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve: Simplifying -11 + -1x = 0 Solving -11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1x = 0 + 11 -1x = 0 + 11 Combine like terms: 0 + 11 = 11 -1x = 11 Divide each side by '-1'. x = -11 Simplifying x = -11Subproblem 2
Set the factor '(13 + -2x)' equal to zero and attempt to solve: Simplifying 13 + -2x = 0 Solving 13 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -2x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2x = 0 + -13 -2x = 0 + -13 Combine like terms: 0 + -13 = -13 -2x = -13 Divide each side by '-2'. x = 6.5 Simplifying x = 6.5Solution
x = {-11, 6.5}
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