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Simplifying (2x + 8)(2x + 10) = 224 Reorder the terms: (8 + 2x)(2x + 10) = 224 Reorder the terms: (8 + 2x)(10 + 2x) = 224 Multiply (8 + 2x) * (10 + 2x) (8(10 + 2x) + 2x * (10 + 2x)) = 224 ((10 * 8 + 2x * 8) + 2x * (10 + 2x)) = 224 ((80 + 16x) + 2x * (10 + 2x)) = 224 (80 + 16x + (10 * 2x + 2x * 2x)) = 224 (80 + 16x + (20x + 4x2)) = 224 Combine like terms: 16x + 20x = 36x (80 + 36x + 4x2) = 224 Solving 80 + 36x + 4x2 = 224 Solving for variable 'x'. Reorder the terms: 80 + -224 + 36x + 4x2 = 224 + -224 Combine like terms: 80 + -224 = -144 -144 + 36x + 4x2 = 224 + -224 Combine like terms: 224 + -224 = 0 -144 + 36x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-36 + 9x + x2) = 0 Factor a trinomial. 4((-12 + -1x)(3 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve: Simplifying -12 + -1x = 0 Solving -12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1x = 0 + 12 -1x = 0 + 12 Combine like terms: 0 + 12 = 12 -1x = 12 Divide each side by '-1'. x = -12 Simplifying x = -12Subproblem 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 = {-12, 3}
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