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Simplifying (w + -6)(w + -6) = 2w2 + -5w + 46 Reorder the terms: (-6 + w)(w + -6) = 2w2 + -5w + 46 Reorder the terms: (-6 + w)(-6 + w) = 2w2 + -5w + 46 Multiply (-6 + w) * (-6 + w) (-6(-6 + w) + w(-6 + w)) = 2w2 + -5w + 46 ((-6 * -6 + w * -6) + w(-6 + w)) = 2w2 + -5w + 46 ((36 + -6w) + w(-6 + w)) = 2w2 + -5w + 46 (36 + -6w + (-6 * w + w * w)) = 2w2 + -5w + 46 (36 + -6w + (-6w + w2)) = 2w2 + -5w + 46 Combine like terms: -6w + -6w = -12w (36 + -12w + w2) = 2w2 + -5w + 46 Reorder the terms: 36 + -12w + w2 = 46 + -5w + 2w2 Solving 36 + -12w + w2 = 46 + -5w + 2w2 Solving for variable 'w'. Reorder the terms: 36 + -46 + -12w + 5w + w2 + -2w2 = 46 + -5w + 2w2 + -46 + 5w + -2w2 Combine like terms: 36 + -46 = -10 -10 + -12w + 5w + w2 + -2w2 = 46 + -5w + 2w2 + -46 + 5w + -2w2 Combine like terms: -12w + 5w = -7w -10 + -7w + w2 + -2w2 = 46 + -5w + 2w2 + -46 + 5w + -2w2 Combine like terms: w2 + -2w2 = -1w2 -10 + -7w + -1w2 = 46 + -5w + 2w2 + -46 + 5w + -2w2 Reorder the terms: -10 + -7w + -1w2 = 46 + -46 + -5w + 5w + 2w2 + -2w2 Combine like terms: 46 + -46 = 0 -10 + -7w + -1w2 = 0 + -5w + 5w + 2w2 + -2w2 -10 + -7w + -1w2 = -5w + 5w + 2w2 + -2w2 Combine like terms: -5w + 5w = 0 -10 + -7w + -1w2 = 0 + 2w2 + -2w2 -10 + -7w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -10 + -7w + -1w2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 7w + w2) = 0 Factor a trinomial. -1((5 + w)(2 + w)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + w)' equal to zero and attempt to solve: Simplifying 5 + w = 0 Solving 5 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + w = 0 + -5 w = 0 + -5 Combine like terms: 0 + -5 = -5 w = -5 Simplifying w = -5Subproblem 2
Set the factor '(2 + w)' equal to zero and attempt to solve: Simplifying 2 + w = 0 Solving 2 + w = 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 + w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + w = 0 + -2 w = 0 + -2 Combine like terms: 0 + -2 = -2 w = -2 Simplifying w = -2Solution
w = {-5, -2}
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