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Simplifying w(w + 6) = 150 Reorder the terms: w(6 + w) = 150 (6 * w + w * w) = 150 (6w + w2) = 150 Solving 6w + w2 = 150 Solving for variable 'w'. Reorder the terms: -150 + 6w + w2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 6w + w2 = 0 Begin completing the square. 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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