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Simplifying (22 + 2x)(14 + 2x) = 560 Multiply (22 + 2x) * (14 + 2x) (22(14 + 2x) + 2x * (14 + 2x)) = 560 ((14 * 22 + 2x * 22) + 2x * (14 + 2x)) = 560 ((308 + 44x) + 2x * (14 + 2x)) = 560 (308 + 44x + (14 * 2x + 2x * 2x)) = 560 (308 + 44x + (28x + 4x2)) = 560 Combine like terms: 44x + 28x = 72x (308 + 72x + 4x2) = 560 Solving 308 + 72x + 4x2 = 560 Solving for variable 'x'. Reorder the terms: 308 + -560 + 72x + 4x2 = 560 + -560 Combine like terms: 308 + -560 = -252 -252 + 72x + 4x2 = 560 + -560 Combine like terms: 560 + -560 = 0 -252 + 72x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-63 + 18x + x2) = 0 Factor a trinomial. 4((-21 + -1x)(3 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-21 + -1x)' equal to zero and attempt to solve: Simplifying -21 + -1x = 0 Solving -21 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + -1x = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -1x = 0 + 21 -1x = 0 + 21 Combine like terms: 0 + 21 = 21 -1x = 21 Divide each side by '-1'. x = -21 Simplifying x = -21Subproblem 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 = {-21, 3}
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