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Simplifying 1060 = (180 + w) * w Reorder the terms for easier multiplication: 1060 = w(180 + w) 1060 = (180 * w + w * w) 1060 = (180w + w2) Solving 1060 = 180w + w2 Solving for variable 'w'. Reorder the terms: 1060 + -180w + -1w2 = 180w + -180w + w2 + -1w2 Combine like terms: 180w + -180w = 0 1060 + -180w + -1w2 = 0 + w2 + -1w2 1060 + -180w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 1060 + -180w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1060 + 180w + w2 = 0 Move the constant term to the right: Add '1060' to each side of the equation. -1060 + 180w + 1060 + w2 = 0 + 1060 Reorder the terms: -1060 + 1060 + 180w + w2 = 0 + 1060 Combine like terms: -1060 + 1060 = 0 0 + 180w + w2 = 0 + 1060 180w + w2 = 0 + 1060 Combine like terms: 0 + 1060 = 1060 180w + w2 = 1060 The w term is 180w. Take half its coefficient (90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. 180w + 8100 + w2 = 1060 + 8100 Reorder the terms: 8100 + 180w + w2 = 1060 + 8100 Combine like terms: 1060 + 8100 = 9160 8100 + 180w + w2 = 9160 Factor a perfect square on the left side: (w + 90)(w + 90) = 9160 Calculate the square root of the right side: 95.707888912 Break this problem into two subproblems by setting (w + 90) equal to 95.707888912 and -95.707888912.Subproblem 1
w + 90 = 95.707888912 Simplifying w + 90 = 95.707888912 Reorder the terms: 90 + w = 95.707888912 Solving 90 + w = 95.707888912 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-90' to each side of the equation. 90 + -90 + w = 95.707888912 + -90 Combine like terms: 90 + -90 = 0 0 + w = 95.707888912 + -90 w = 95.707888912 + -90 Combine like terms: 95.707888912 + -90 = 5.707888912 w = 5.707888912 Simplifying w = 5.707888912Subproblem 2
w + 90 = -95.707888912 Simplifying w + 90 = -95.707888912 Reorder the terms: 90 + w = -95.707888912 Solving 90 + w = -95.707888912 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-90' to each side of the equation. 90 + -90 + w = -95.707888912 + -90 Combine like terms: 90 + -90 = 0 0 + w = -95.707888912 + -90 w = -95.707888912 + -90 Combine like terms: -95.707888912 + -90 = -185.707888912 w = -185.707888912 Simplifying w = -185.707888912Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.707888912, -185.707888912}
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