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Simplifying (14 + 2x)(28 + x) = 792 Multiply (14 + 2x) * (28 + x) (14(28 + x) + 2x * (28 + x)) = 792 ((28 * 14 + x * 14) + 2x * (28 + x)) = 792 ((392 + 14x) + 2x * (28 + x)) = 792 (392 + 14x + (28 * 2x + x * 2x)) = 792 (392 + 14x + (56x + 2x2)) = 792 Combine like terms: 14x + 56x = 70x (392 + 70x + 2x2) = 792 Solving 392 + 70x + 2x2 = 792 Solving for variable 'x'. Reorder the terms: 392 + -792 + 70x + 2x2 = 792 + -792 Combine like terms: 392 + -792 = -400 -400 + 70x + 2x2 = 792 + -792 Combine like terms: 792 + -792 = 0 -400 + 70x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-200 + 35x + x2) = 0 Factor a trinomial. 2((-40 + -1x)(5 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-40 + -1x)' equal to zero and attempt to solve: Simplifying -40 + -1x = 0 Solving -40 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + -1x = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -1x = 0 + 40 -1x = 0 + 40 Combine like terms: 0 + 40 = 40 -1x = 40 Divide each side by '-1'. x = -40 Simplifying x = -40Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-40, 5}
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