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Simplifying (2w + -8)(w) = 234 Reorder the terms: (-8 + 2w)(w) = 234 Reorder the terms for easier multiplication: w(-8 + 2w) = 234 (-8 * w + 2w * w) = 234 (-8w + 2w2) = 234 Solving -8w + 2w2 = 234 Solving for variable 'w'. Reorder the terms: -234 + -8w + 2w2 = 234 + -234 Combine like terms: 234 + -234 = 0 -234 + -8w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-117 + -4w + w2) = 0 Factor a trinomial. 2((-9 + -1w)(13 + -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 '(13 + -1w)' equal to zero and attempt to solve: Simplifying 13 + -1w = 0 Solving 13 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1w = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1w = 0 + -13 -1w = 0 + -13 Combine like terms: 0 + -13 = -13 -1w = -13 Divide each side by '-1'. w = 13 Simplifying w = 13Solution
w = {-9, 13}
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