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Simplifying 150 = (w + 6) * w Reorder the terms: 150 = (6 + w) * w Reorder the terms for easier multiplication: 150 = w(6 + w) 150 = (6 * w + w * w) 150 = (6w + w2) Solving 150 = 6w + w2 Solving for variable 'w'. Reorder the terms: 150 + -6w + -1w2 = 6w + -6w + w2 + -1w2 Combine like terms: 6w + -6w = 0 150 + -6w + -1w2 = 0 + w2 + -1w2 150 + -6w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 150 + -6w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -150 + 6w + w2 = 0 Move the constant term to the right: Add '150' to each side of the equation. -150 + 6w + 150 + w2 = 0 + 150 Reorder the terms: -150 + 150 + 6w + w2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 6w + w2 = 0 + 150 6w + w2 = 0 + 150 Combine like terms: 0 + 150 = 150 6w + w2 = 150 The w term is 6w. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6w + 9 + w2 = 150 + 9 Reorder the terms: 9 + 6w + w2 = 150 + 9 Combine like terms: 150 + 9 = 159 9 + 6w + w2 = 159 Factor a perfect square on the left side: (w + 3)(w + 3) = 159 Calculate the square root of the right side: 12.609520213 Break this problem into two subproblems by setting (w + 3) equal to 12.609520213 and -12.609520213.Subproblem 1
w + 3 = 12.609520213 Simplifying w + 3 = 12.609520213 Reorder the terms: 3 + w = 12.609520213 Solving 3 + w = 12.609520213 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 12.609520213 + -3 Combine like terms: 3 + -3 = 0 0 + w = 12.609520213 + -3 w = 12.609520213 + -3 Combine like terms: 12.609520213 + -3 = 9.609520213 w = 9.609520213 Simplifying w = 9.609520213Subproblem 2
w + 3 = -12.609520213 Simplifying w + 3 = -12.609520213 Reorder the terms: 3 + w = -12.609520213 Solving 3 + w = -12.609520213 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = -12.609520213 + -3 Combine like terms: 3 + -3 = 0 0 + w = -12.609520213 + -3 w = -12.609520213 + -3 Combine like terms: -12.609520213 + -3 = -15.609520213 w = -15.609520213 Simplifying w = -15.609520213Solution
The solution to the problem is based on the solutions from the subproblems. w = {9.609520213, -15.609520213}
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