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Simplifying 88 = (12 + -2x)(15 + -2x) Multiply (12 + -2x) * (15 + -2x) 88 = (12(15 + -2x) + -2x * (15 + -2x)) 88 = ((15 * 12 + -2x * 12) + -2x * (15 + -2x)) 88 = ((180 + -24x) + -2x * (15 + -2x)) 88 = (180 + -24x + (15 * -2x + -2x * -2x)) 88 = (180 + -24x + (-30x + 4x2)) Combine like terms: -24x + -30x = -54x 88 = (180 + -54x + 4x2) Solving 88 = 180 + -54x + 4x2 Solving for variable 'x'. Combine like terms: 88 + -180 = -92 -92 + 54x + -4x2 = 180 + -54x + 4x2 + -180 + 54x + -4x2 Reorder the terms: -92 + 54x + -4x2 = 180 + -180 + -54x + 54x + 4x2 + -4x2 Combine like terms: 180 + -180 = 0 -92 + 54x + -4x2 = 0 + -54x + 54x + 4x2 + -4x2 -92 + 54x + -4x2 = -54x + 54x + 4x2 + -4x2 Combine like terms: -54x + 54x = 0 -92 + 54x + -4x2 = 0 + 4x2 + -4x2 -92 + 54x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -92 + 54x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-46 + 27x + -2x2) = 0 Factor a trinomial. 2((-23 + 2x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-23 + 2x)' equal to zero and attempt to solve: Simplifying -23 + 2x = 0 Solving -23 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + 2x = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 2x = 0 + 23 2x = 0 + 23 Combine like terms: 0 + 23 = 23 2x = 23 Divide each side by '2'. x = 11.5 Simplifying x = 11.5Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {11.5, 2}
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