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Simplifying w2 = 14 + -15w Solving w2 = 14 + -15w Solving for variable 'w'. Reorder the terms: -14 + 15w + w2 = 14 + -15w + -14 + 15w Reorder the terms: -14 + 15w + w2 = 14 + -14 + -15w + 15w Combine like terms: 14 + -14 = 0 -14 + 15w + w2 = 0 + -15w + 15w -14 + 15w + w2 = -15w + 15w Combine like terms: -15w + 15w = 0 -14 + 15w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 15w + 14 + w2 = 0 + 14 Reorder the terms: -14 + 14 + 15w + w2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 15w + w2 = 0 + 14 15w + w2 = 0 + 14 Combine like terms: 0 + 14 = 14 15w + w2 = 14 The w term is 15w. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15w + 56.25 + w2 = 14 + 56.25 Reorder the terms: 56.25 + 15w + w2 = 14 + 56.25 Combine like terms: 14 + 56.25 = 70.25 56.25 + 15w + w2 = 70.25 Factor a perfect square on the left side: (w + 7.5)(w + 7.5) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (w + 7.5) equal to 8.381527307 and -8.381527307.Subproblem 1
w + 7.5 = 8.381527307 Simplifying w + 7.5 = 8.381527307 Reorder the terms: 7.5 + w = 8.381527307 Solving 7.5 + w = 8.381527307 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + w = 8.381527307 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = 8.381527307 + -7.5 w = 8.381527307 + -7.5 Combine like terms: 8.381527307 + -7.5 = 0.881527307 w = 0.881527307 Simplifying w = 0.881527307Subproblem 2
w + 7.5 = -8.381527307 Simplifying w + 7.5 = -8.381527307 Reorder the terms: 7.5 + w = -8.381527307 Solving 7.5 + w = -8.381527307 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + w = -8.381527307 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = -8.381527307 + -7.5 w = -8.381527307 + -7.5 Combine like terms: -8.381527307 + -7.5 = -15.881527307 w = -15.881527307 Simplifying w = -15.881527307Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.881527307, -15.881527307}
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