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Simplifying 2w2 + -6w + 41 = (w + -6)(w + -6) Reorder the terms: 41 + -6w + 2w2 = (w + -6)(w + -6) Reorder the terms: 41 + -6w + 2w2 = (-6 + w)(w + -6) Reorder the terms: 41 + -6w + 2w2 = (-6 + w)(-6 + w) Multiply (-6 + w) * (-6 + w) 41 + -6w + 2w2 = (-6(-6 + w) + w(-6 + w)) 41 + -6w + 2w2 = ((-6 * -6 + w * -6) + w(-6 + w)) 41 + -6w + 2w2 = ((36 + -6w) + w(-6 + w)) 41 + -6w + 2w2 = (36 + -6w + (-6 * w + w * w)) 41 + -6w + 2w2 = (36 + -6w + (-6w + w2)) Combine like terms: -6w + -6w = -12w 41 + -6w + 2w2 = (36 + -12w + w2) Solving 41 + -6w + 2w2 = 36 + -12w + w2 Solving for variable 'w'. Reorder the terms: 41 + -36 + -6w + 12w + 2w2 + -1w2 = 36 + -12w + w2 + -36 + 12w + -1w2 Combine like terms: 41 + -36 = 5 5 + -6w + 12w + 2w2 + -1w2 = 36 + -12w + w2 + -36 + 12w + -1w2 Combine like terms: -6w + 12w = 6w 5 + 6w + 2w2 + -1w2 = 36 + -12w + w2 + -36 + 12w + -1w2 Combine like terms: 2w2 + -1w2 = 1w2 5 + 6w + 1w2 = 36 + -12w + w2 + -36 + 12w + -1w2 Reorder the terms: 5 + 6w + 1w2 = 36 + -36 + -12w + 12w + w2 + -1w2 Combine like terms: 36 + -36 = 0 5 + 6w + 1w2 = 0 + -12w + 12w + w2 + -1w2 5 + 6w + 1w2 = -12w + 12w + w2 + -1w2 Combine like terms: -12w + 12w = 0 5 + 6w + 1w2 = 0 + w2 + -1w2 5 + 6w + 1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 5 + 6w + 1w2 = 0 Factor a trinomial. (5 + w)(1 + w) = 0Subproblem 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 '(1 + w)' equal to zero and attempt to solve: Simplifying 1 + w = 0 Solving 1 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + w = 0 + -1 w = 0 + -1 Combine like terms: 0 + -1 = -1 w = -1 Simplifying w = -1Solution
w = {-5, -1}
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