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Simplifying w2 = 8w + 72 Reorder the terms: w2 = 72 + 8w Solving w2 = 72 + 8w Solving for variable 'w'. Reorder the terms: -72 + -8w + w2 = 72 + 8w + -72 + -8w Reorder the terms: -72 + -8w + w2 = 72 + -72 + 8w + -8w Combine like terms: 72 + -72 = 0 -72 + -8w + w2 = 0 + 8w + -8w -72 + -8w + w2 = 8w + -8w Combine like terms: 8w + -8w = 0 -72 + -8w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -8w + 72 + w2 = 0 + 72 Reorder the terms: -72 + 72 + -8w + w2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -8w + w2 = 0 + 72 -8w + w2 = 0 + 72 Combine like terms: 0 + 72 = 72 -8w + w2 = 72 The w term is -8w. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8w + 16 + w2 = 72 + 16 Reorder the terms: 16 + -8w + w2 = 72 + 16 Combine like terms: 72 + 16 = 88 16 + -8w + w2 = 88 Factor a perfect square on the left side: (w + -4)(w + -4) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (w + -4) equal to 9.38083152 and -9.38083152.Subproblem 1
w + -4 = 9.38083152 Simplifying w + -4 = 9.38083152 Reorder the terms: -4 + w = 9.38083152 Solving -4 + w = 9.38083152 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = 9.38083152 + 4 Combine like terms: -4 + 4 = 0 0 + w = 9.38083152 + 4 w = 9.38083152 + 4 Combine like terms: 9.38083152 + 4 = 13.38083152 w = 13.38083152 Simplifying w = 13.38083152Subproblem 2
w + -4 = -9.38083152 Simplifying w + -4 = -9.38083152 Reorder the terms: -4 + w = -9.38083152 Solving -4 + w = -9.38083152 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = -9.38083152 + 4 Combine like terms: -4 + 4 = 0 0 + w = -9.38083152 + 4 w = -9.38083152 + 4 Combine like terms: -9.38083152 + 4 = -5.38083152 w = -5.38083152 Simplifying w = -5.38083152Solution
The solution to the problem is based on the solutions from the subproblems. w = {13.38083152, -5.38083152}
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