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Simplifying (w + -5)(w + -5) = 2w2 + -21w + 55 Reorder the terms: (-5 + w)(w + -5) = 2w2 + -21w + 55 Reorder the terms: (-5 + w)(-5 + w) = 2w2 + -21w + 55 Multiply (-5 + w) * (-5 + w) (-5(-5 + w) + w(-5 + w)) = 2w2 + -21w + 55 ((-5 * -5 + w * -5) + w(-5 + w)) = 2w2 + -21w + 55 ((25 + -5w) + w(-5 + w)) = 2w2 + -21w + 55 (25 + -5w + (-5 * w + w * w)) = 2w2 + -21w + 55 (25 + -5w + (-5w + w2)) = 2w2 + -21w + 55 Combine like terms: -5w + -5w = -10w (25 + -10w + w2) = 2w2 + -21w + 55 Reorder the terms: 25 + -10w + w2 = 55 + -21w + 2w2 Solving 25 + -10w + w2 = 55 + -21w + 2w2 Solving for variable 'w'. Reorder the terms: 25 + -55 + -10w + 21w + w2 + -2w2 = 55 + -21w + 2w2 + -55 + 21w + -2w2 Combine like terms: 25 + -55 = -30 -30 + -10w + 21w + w2 + -2w2 = 55 + -21w + 2w2 + -55 + 21w + -2w2 Combine like terms: -10w + 21w = 11w -30 + 11w + w2 + -2w2 = 55 + -21w + 2w2 + -55 + 21w + -2w2 Combine like terms: w2 + -2w2 = -1w2 -30 + 11w + -1w2 = 55 + -21w + 2w2 + -55 + 21w + -2w2 Reorder the terms: -30 + 11w + -1w2 = 55 + -55 + -21w + 21w + 2w2 + -2w2 Combine like terms: 55 + -55 = 0 -30 + 11w + -1w2 = 0 + -21w + 21w + 2w2 + -2w2 -30 + 11w + -1w2 = -21w + 21w + 2w2 + -2w2 Combine like terms: -21w + 21w = 0 -30 + 11w + -1w2 = 0 + 2w2 + -2w2 -30 + 11w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -30 + 11w + -1w2 = 0 Factor a trinomial. (-6 + w)(5 + -1w) = 0Subproblem 1
Set the factor '(-6 + w)' equal to zero and attempt to solve: Simplifying -6 + w = 0 Solving -6 + w = 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 + w = 0 + 6 Combine like terms: -6 + 6 = 0 0 + w = 0 + 6 w = 0 + 6 Combine like terms: 0 + 6 = 6 w = 6 Simplifying w = 6Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve: Simplifying 5 + -1w = 0 Solving 5 + -1w = 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 + -1w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1w = 0 + -5 -1w = 0 + -5 Combine like terms: 0 + -5 = -5 -1w = -5 Divide each side by '-1'. w = 5 Simplifying w = 5Solution
w = {6, 5}
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