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Simplifying 2(w + 11)(w + -5) = 100 + w(w + 11) Reorder the terms: 2(11 + w)(w + -5) = 100 + w(w + 11) Reorder the terms: 2(11 + w)(-5 + w) = 100 + w(w + 11) Multiply (11 + w) * (-5 + w) 2(11(-5 + w) + w(-5 + w)) = 100 + w(w + 11) 2((-5 * 11 + w * 11) + w(-5 + w)) = 100 + w(w + 11) 2((-55 + 11w) + w(-5 + w)) = 100 + w(w + 11) 2(-55 + 11w + (-5 * w + w * w)) = 100 + w(w + 11) 2(-55 + 11w + (-5w + w2)) = 100 + w(w + 11) Combine like terms: 11w + -5w = 6w 2(-55 + 6w + w2) = 100 + w(w + 11) (-55 * 2 + 6w * 2 + w2 * 2) = 100 + w(w + 11) (-110 + 12w + 2w2) = 100 + w(w + 11) Reorder the terms: -110 + 12w + 2w2 = 100 + w(11 + w) -110 + 12w + 2w2 = 100 + (11 * w + w * w) -110 + 12w + 2w2 = 100 + (11w + w2) Solving -110 + 12w + 2w2 = 100 + 11w + w2 Solving for variable 'w'. Reorder the terms: -110 + -100 + 12w + -11w + 2w2 + -1w2 = 100 + 11w + w2 + -100 + -11w + -1w2 Combine like terms: -110 + -100 = -210 -210 + 12w + -11w + 2w2 + -1w2 = 100 + 11w + w2 + -100 + -11w + -1w2 Combine like terms: 12w + -11w = 1w -210 + 1w + 2w2 + -1w2 = 100 + 11w + w2 + -100 + -11w + -1w2 Combine like terms: 2w2 + -1w2 = 1w2 -210 + 1w + 1w2 = 100 + 11w + w2 + -100 + -11w + -1w2 Reorder the terms: -210 + 1w + 1w2 = 100 + -100 + 11w + -11w + w2 + -1w2 Combine like terms: 100 + -100 = 0 -210 + 1w + 1w2 = 0 + 11w + -11w + w2 + -1w2 -210 + 1w + 1w2 = 11w + -11w + w2 + -1w2 Combine like terms: 11w + -11w = 0 -210 + 1w + 1w2 = 0 + w2 + -1w2 -210 + 1w + 1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -210 + 1w + 1w2 = 0 Factor a trinomial. (-15 + -1w)(14 + -1w) = 0Subproblem 1
Set the factor '(-15 + -1w)' equal to zero and attempt to solve: Simplifying -15 + -1w = 0 Solving -15 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1w = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1w = 0 + 15 -1w = 0 + 15 Combine like terms: 0 + 15 = 15 -1w = 15 Divide each side by '-1'. w = -15 Simplifying w = -15Subproblem 2
Set the factor '(14 + -1w)' equal to zero and attempt to solve: Simplifying 14 + -1w = 0 Solving 14 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1w = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1w = 0 + -14 -1w = 0 + -14 Combine like terms: 0 + -14 = -14 -1w = -14 Divide each side by '-1'. w = 14 Simplifying w = 14Solution
w = {-15, 14}
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