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Simplifying (w)(w + -1) + -1w + -22 = (w + 5)(w + -5) Reorder the terms: w(-1 + w) + -1w + -22 = (w + 5)(w + -5) (-1 * w + w * w) + -1w + -22 = (w + 5)(w + -5) (-1w + w2) + -1w + -22 = (w + 5)(w + -5) Reorder the terms: -22 + -1w + -1w + w2 = (w + 5)(w + -5) Combine like terms: -1w + -1w = -2w -22 + -2w + w2 = (w + 5)(w + -5) Reorder the terms: -22 + -2w + w2 = (5 + w)(w + -5) Reorder the terms: -22 + -2w + w2 = (5 + w)(-5 + w) Multiply (5 + w) * (-5 + w) -22 + -2w + w2 = (5(-5 + w) + w(-5 + w)) -22 + -2w + w2 = ((-5 * 5 + w * 5) + w(-5 + w)) -22 + -2w + w2 = ((-25 + 5w) + w(-5 + w)) -22 + -2w + w2 = (-25 + 5w + (-5 * w + w * w)) -22 + -2w + w2 = (-25 + 5w + (-5w + w2)) Combine like terms: 5w + -5w = 0 -22 + -2w + w2 = (-25 + 0 + w2) -22 + -2w + w2 = (-25 + w2) Add '-1w2' to each side of the equation. -22 + -2w + w2 + -1w2 = -25 + w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -22 + -2w + 0 = -25 + w2 + -1w2 -22 + -2w = -25 + w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -22 + -2w = -25 + 0 -22 + -2w = -25 Solving -22 + -2w = -25 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + -2w = -25 + 22 Combine like terms: -22 + 22 = 0 0 + -2w = -25 + 22 -2w = -25 + 22 Combine like terms: -25 + 22 = -3 -2w = -3 Divide each side by '-2'. w = 1.5 Simplifying w = 1.5
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