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Simplifying 88 = w(w + 5) Reorder the terms: 88 = w(5 + w) 88 = (5 * w + w * w) 88 = (5w + w2) Solving 88 = 5w + w2 Solving for variable 'w'. Reorder the terms: 88 + -5w + -1w2 = 5w + -5w + w2 + -1w2 Combine like terms: 5w + -5w = 0 88 + -5w + -1w2 = 0 + w2 + -1w2 88 + -5w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 88 + -5w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -88 + 5w + w2 = 0 Move the constant term to the right: Add '88' to each side of the equation. -88 + 5w + 88 + w2 = 0 + 88 Reorder the terms: -88 + 88 + 5w + w2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + 5w + w2 = 0 + 88 5w + w2 = 0 + 88 Combine like terms: 0 + 88 = 88 5w + w2 = 88 The w term is 5w. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5w + 6.25 + w2 = 88 + 6.25 Reorder the terms: 6.25 + 5w + w2 = 88 + 6.25 Combine like terms: 88 + 6.25 = 94.25 6.25 + 5w + w2 = 94.25 Factor a perfect square on the left side: (w + 2.5)(w + 2.5) = 94.25 Calculate the square root of the right side: 9.708243919 Break this problem into two subproblems by setting (w + 2.5) equal to 9.708243919 and -9.708243919.Subproblem 1
w + 2.5 = 9.708243919 Simplifying w + 2.5 = 9.708243919 Reorder the terms: 2.5 + w = 9.708243919 Solving 2.5 + w = 9.708243919 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = 9.708243919 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = 9.708243919 + -2.5 w = 9.708243919 + -2.5 Combine like terms: 9.708243919 + -2.5 = 7.208243919 w = 7.208243919 Simplifying w = 7.208243919Subproblem 2
w + 2.5 = -9.708243919 Simplifying w + 2.5 = -9.708243919 Reorder the terms: 2.5 + w = -9.708243919 Solving 2.5 + w = -9.708243919 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = -9.708243919 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = -9.708243919 + -2.5 w = -9.708243919 + -2.5 Combine like terms: -9.708243919 + -2.5 = -12.208243919 w = -12.208243919 Simplifying w = -12.208243919Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.208243919, -12.208243919}
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