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Simplifying (w)(2w + 2) = 84 Reorder the terms: w(2 + 2w) = 84 (2 * w + 2w * w) = 84 (2w + 2w2) = 84 Solving 2w + 2w2 = 84 Solving for variable 'w'. Reorder the terms: -84 + 2w + 2w2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + 2w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-42 + w + w2) = 0 Factor a trinomial. 2((-7 + -1w)(6 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -1w)' equal to zero and attempt to solve: Simplifying -7 + -1w = 0 Solving -7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1w = 0 + 7 -1w = 0 + 7 Combine like terms: 0 + 7 = 7 -1w = 7 Divide each side by '-1'. w = -7 Simplifying w = -7Subproblem 2
Set the factor '(6 + -1w)' equal to zero and attempt to solve: Simplifying 6 + -1w = 0 Solving 6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1w = 0 + -6 -1w = 0 + -6 Combine like terms: 0 + -6 = -6 -1w = -6 Divide each side by '-1'. w = 6 Simplifying w = 6Solution
w = {-7, 6}
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