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Simplifying (14 + 2x)(30 + 2x) = 1092 Multiply (14 + 2x) * (30 + 2x) (14(30 + 2x) + 2x * (30 + 2x)) = 1092 ((30 * 14 + 2x * 14) + 2x * (30 + 2x)) = 1092 ((420 + 28x) + 2x * (30 + 2x)) = 1092 (420 + 28x + (30 * 2x + 2x * 2x)) = 1092 (420 + 28x + (60x + 4x2)) = 1092 Combine like terms: 28x + 60x = 88x (420 + 88x + 4x2) = 1092 Solving 420 + 88x + 4x2 = 1092 Solving for variable 'x'. Reorder the terms: 420 + -1092 + 88x + 4x2 = 1092 + -1092 Combine like terms: 420 + -1092 = -672 -672 + 88x + 4x2 = 1092 + -1092 Combine like terms: 1092 + -1092 = 0 -672 + 88x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-168 + 22x + x2) = 0 Factor a trinomial. 4((-28 + -1x)(6 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-28 + -1x)' equal to zero and attempt to solve: Simplifying -28 + -1x = 0 Solving -28 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + -1x = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -1x = 0 + 28 -1x = 0 + 28 Combine like terms: 0 + 28 = 28 -1x = 28 Divide each side by '-1'. x = -28 Simplifying x = -28Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-28, 6}
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