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Simplifying (18 + -1x)(18 + -1x) + -2(18 + -1x) * x = 0 Multiply (18 + -1x) * (18 + -1x) (18(18 + -1x) + -1x * (18 + -1x)) + -2(18 + -1x) * x = 0 ((18 * 18 + -1x * 18) + -1x * (18 + -1x)) + -2(18 + -1x) * x = 0 ((324 + -18x) + -1x * (18 + -1x)) + -2(18 + -1x) * x = 0 (324 + -18x + (18 * -1x + -1x * -1x)) + -2(18 + -1x) * x = 0 (324 + -18x + (-18x + 1x2)) + -2(18 + -1x) * x = 0 Combine like terms: -18x + -18x = -36x (324 + -36x + 1x2) + -2(18 + -1x) * x = 0 Reorder the terms for easier multiplication: 324 + -36x + 1x2 + -2x(18 + -1x) = 0 324 + -36x + 1x2 + (18 * -2x + -1x * -2x) = 0 324 + -36x + 1x2 + (-36x + 2x2) = 0 Reorder the terms: 324 + -36x + -36x + 1x2 + 2x2 = 0 Combine like terms: -36x + -36x = -72x 324 + -72x + 1x2 + 2x2 = 0 Combine like terms: 1x2 + 2x2 = 3x2 324 + -72x + 3x2 = 0 Solving 324 + -72x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(108 + -24x + x2) = 0 Factor a trinomial. 3((6 + -1x)(18 + -1x)) = 0 Ignore the factor 3.Subproblem 1
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 = 6Subproblem 2
Set the factor '(18 + -1x)' equal to zero and attempt to solve: Simplifying 18 + -1x = 0 Solving 18 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1x = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1x = 0 + -18 -1x = 0 + -18 Combine like terms: 0 + -18 = -18 -1x = -18 Divide each side by '-1'. x = 18 Simplifying x = 18Solution
x = {6, 18}
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