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Simplifying (42 + 2x)(20 + 2x) = 1248 Multiply (42 + 2x) * (20 + 2x) (42(20 + 2x) + 2x * (20 + 2x)) = 1248 ((20 * 42 + 2x * 42) + 2x * (20 + 2x)) = 1248 ((840 + 84x) + 2x * (20 + 2x)) = 1248 (840 + 84x + (20 * 2x + 2x * 2x)) = 1248 (840 + 84x + (40x + 4x2)) = 1248 Combine like terms: 84x + 40x = 124x (840 + 124x + 4x2) = 1248 Solving 840 + 124x + 4x2 = 1248 Solving for variable 'x'. Reorder the terms: 840 + -1248 + 124x + 4x2 = 1248 + -1248 Combine like terms: 840 + -1248 = -408 -408 + 124x + 4x2 = 1248 + -1248 Combine like terms: 1248 + -1248 = 0 -408 + 124x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-102 + 31x + x2) = 0 Factor a trinomial. 4((-34 + -1x)(3 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-34 + -1x)' equal to zero and attempt to solve: Simplifying -34 + -1x = 0 Solving -34 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '34' to each side of the equation. -34 + 34 + -1x = 0 + 34 Combine like terms: -34 + 34 = 0 0 + -1x = 0 + 34 -1x = 0 + 34 Combine like terms: 0 + 34 = 34 -1x = 34 Divide each side by '-1'. x = -34 Simplifying x = -34Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-34, 3}
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