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Simplifying (w + -4)(w + 6 + -4) * 2 = 182 Reorder the terms: (-4 + w)(w + 6 + -4) * 2 = 182 Reorder the terms: (-4 + w)(6 + -4 + w) * 2 = 182 Combine like terms: 6 + -4 = 2 (-4 + w)(2 + w) * 2 = 182 Reorder the terms for easier multiplication: 2(-4 + w)(2 + w) = 182 Multiply (-4 + w) * (2 + w) 2(-4(2 + w) + w(2 + w)) = 182 2((2 * -4 + w * -4) + w(2 + w)) = 182 2((-8 + -4w) + w(2 + w)) = 182 2(-8 + -4w + (2 * w + w * w)) = 182 2(-8 + -4w + (2w + w2)) = 182 Combine like terms: -4w + 2w = -2w 2(-8 + -2w + w2) = 182 (-8 * 2 + -2w * 2 + w2 * 2) = 182 (-16 + -4w + 2w2) = 182 Solving -16 + -4w + 2w2 = 182 Solving for variable 'w'. Reorder the terms: -16 + -182 + -4w + 2w2 = 182 + -182 Combine like terms: -16 + -182 = -198 -198 + -4w + 2w2 = 182 + -182 Combine like terms: 182 + -182 = 0 -198 + -4w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-99 + -2w + w2) = 0 Factor a trinomial. 2((-9 + -1w)(11 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -1w)' equal to zero and attempt to solve: Simplifying -9 + -1w = 0 Solving -9 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1w = 0 + 9 -1w = 0 + 9 Combine like terms: 0 + 9 = 9 -1w = 9 Divide each side by '-1'. w = -9 Simplifying w = -9Subproblem 2
Set the factor '(11 + -1w)' equal to zero and attempt to solve: Simplifying 11 + -1w = 0 Solving 11 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1w = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1w = 0 + -11 -1w = 0 + -11 Combine like terms: 0 + -11 = -11 -1w = -11 Divide each side by '-1'. w = 11 Simplifying w = 11Solution
w = {-9, 11}
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