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Simplifying (44 + 2x)(59 + 2x) = 1504 Multiply (44 + 2x) * (59 + 2x) (44(59 + 2x) + 2x * (59 + 2x)) = 1504 ((59 * 44 + 2x * 44) + 2x * (59 + 2x)) = 1504 ((2596 + 88x) + 2x * (59 + 2x)) = 1504 (2596 + 88x + (59 * 2x + 2x * 2x)) = 1504 (2596 + 88x + (118x + 4x2)) = 1504 Combine like terms: 88x + 118x = 206x (2596 + 206x + 4x2) = 1504 Solving 2596 + 206x + 4x2 = 1504 Solving for variable 'x'. Reorder the terms: 2596 + -1504 + 206x + 4x2 = 1504 + -1504 Combine like terms: 2596 + -1504 = 1092 1092 + 206x + 4x2 = 1504 + -1504 Combine like terms: 1504 + -1504 = 0 1092 + 206x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(546 + 103x + 2x2) = 0 Factor a trinomial. 2((91 + 2x)(6 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(91 + 2x)' equal to zero and attempt to solve: Simplifying 91 + 2x = 0 Solving 91 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-91' to each side of the equation. 91 + -91 + 2x = 0 + -91 Combine like terms: 91 + -91 = 0 0 + 2x = 0 + -91 2x = 0 + -91 Combine like terms: 0 + -91 = -91 2x = -91 Divide each side by '2'. x = -45.5 Simplifying x = -45.5Subproblem 2
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 = -6Solution
x = {-45.5, -6}
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