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Simplifying 28 = (10 + 2w)(w) Reorder the terms for easier multiplication: 28 = w(10 + 2w) 28 = (10 * w + 2w * w) 28 = (10w + 2w2) Solving 28 = 10w + 2w2 Solving for variable 'w'. Reorder the terms: 28 + -10w + -2w2 = 10w + -10w + 2w2 + -2w2 Combine like terms: 10w + -10w = 0 28 + -10w + -2w2 = 0 + 2w2 + -2w2 28 + -10w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 28 + -10w + -2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(14 + -5w + -1w2) = 0 Factor a trinomial. 2((2 + -1w)(7 + w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -1w)' equal to zero and attempt to solve: Simplifying 2 + -1w = 0 Solving 2 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w = 0 + -2 -1w = 0 + -2 Combine like terms: 0 + -2 = -2 -1w = -2 Divide each side by '-1'. w = 2 Simplifying w = 2Subproblem 2
Set the factor '(7 + w)' equal to zero and attempt to solve: Simplifying 7 + w = 0 Solving 7 + w = 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 + w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + w = 0 + -7 w = 0 + -7 Combine like terms: 0 + -7 = -7 w = -7 Simplifying w = -7Solution
w = {2, -7}
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