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Simplifying (w + 7)(w + 7) + -46 = 75 Reorder the terms: (7 + w)(w + 7) + -46 = 75 Reorder the terms: (7 + w)(7 + w) + -46 = 75 Multiply (7 + w) * (7 + w) (7(7 + w) + w(7 + w)) + -46 = 75 ((7 * 7 + w * 7) + w(7 + w)) + -46 = 75 ((49 + 7w) + w(7 + w)) + -46 = 75 (49 + 7w + (7 * w + w * w)) + -46 = 75 (49 + 7w + (7w + w2)) + -46 = 75 Combine like terms: 7w + 7w = 14w (49 + 14w + w2) + -46 = 75 Reorder the terms: 49 + -46 + 14w + w2 = 75 Combine like terms: 49 + -46 = 3 3 + 14w + w2 = 75 Solving 3 + 14w + w2 = 75 Solving for variable 'w'. Reorder the terms: 3 + -75 + 14w + w2 = 75 + -75 Combine like terms: 3 + -75 = -72 -72 + 14w + w2 = 75 + -75 Combine like terms: 75 + -75 = 0 -72 + 14w + w2 = 0 Factor a trinomial. (-18 + -1w)(4 + -1w) = 0Subproblem 1
Set the factor '(-18 + -1w)' equal to zero and attempt to solve: Simplifying -18 + -1w = 0 Solving -18 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + -1w = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -1w = 0 + 18 -1w = 0 + 18 Combine like terms: 0 + 18 = 18 -1w = 18 Divide each side by '-1'. w = -18 Simplifying w = -18Subproblem 2
Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4Solution
w = {-18, 4}
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