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Simplifying w2 + 8w = 230 Reorder the terms: 8w + w2 = 230 Solving 8w + w2 = 230 Solving for variable 'w'. Reorder the terms: -230 + 8w + w2 = 230 + -230 Combine like terms: 230 + -230 = 0 -230 + 8w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '230' to each side of the equation. -230 + 8w + 230 + w2 = 0 + 230 Reorder the terms: -230 + 230 + 8w + w2 = 0 + 230 Combine like terms: -230 + 230 = 0 0 + 8w + w2 = 0 + 230 8w + w2 = 0 + 230 Combine like terms: 0 + 230 = 230 8w + w2 = 230 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 = 230 + 16 Reorder the terms: 16 + 8w + w2 = 230 + 16 Combine like terms: 230 + 16 = 246 16 + 8w + w2 = 246 Factor a perfect square on the left side: (w + 4)(w + 4) = 246 Calculate the square root of the right side: 15.684387141 Break this problem into two subproblems by setting (w + 4) equal to 15.684387141 and -15.684387141.Subproblem 1
w + 4 = 15.684387141 Simplifying w + 4 = 15.684387141 Reorder the terms: 4 + w = 15.684387141 Solving 4 + w = 15.684387141 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 = 15.684387141 + -4 Combine like terms: 4 + -4 = 0 0 + w = 15.684387141 + -4 w = 15.684387141 + -4 Combine like terms: 15.684387141 + -4 = 11.684387141 w = 11.684387141 Simplifying w = 11.684387141Subproblem 2
w + 4 = -15.684387141 Simplifying w + 4 = -15.684387141 Reorder the terms: 4 + w = -15.684387141 Solving 4 + w = -15.684387141 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 = -15.684387141 + -4 Combine like terms: 4 + -4 = 0 0 + w = -15.684387141 + -4 w = -15.684387141 + -4 Combine like terms: -15.684387141 + -4 = -19.684387141 w = -19.684387141 Simplifying w = -19.684387141Solution
The solution to the problem is based on the solutions from the subproblems. w = {11.684387141, -19.684387141}
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