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Simplifying w2 + 6w + -116 = 0 Reorder the terms: -116 + 6w + w2 = 0 Solving -116 + 6w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '116' to each side of the equation. -116 + 6w + 116 + w2 = 0 + 116 Reorder the terms: -116 + 116 + 6w + w2 = 0 + 116 Combine like terms: -116 + 116 = 0 0 + 6w + w2 = 0 + 116 6w + w2 = 0 + 116 Combine like terms: 0 + 116 = 116 6w + w2 = 116 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 = 116 + 9 Reorder the terms: 9 + 6w + w2 = 116 + 9 Combine like terms: 116 + 9 = 125 9 + 6w + w2 = 125 Factor a perfect square on the left side: (w + 3)(w + 3) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (w + 3) equal to 11.180339887 and -11.180339887.Subproblem 1
w + 3 = 11.180339887 Simplifying w + 3 = 11.180339887 Reorder the terms: 3 + w = 11.180339887 Solving 3 + w = 11.180339887 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 = 11.180339887 + -3 Combine like terms: 3 + -3 = 0 0 + w = 11.180339887 + -3 w = 11.180339887 + -3 Combine like terms: 11.180339887 + -3 = 8.180339887 w = 8.180339887 Simplifying w = 8.180339887Subproblem 2
w + 3 = -11.180339887 Simplifying w + 3 = -11.180339887 Reorder the terms: 3 + w = -11.180339887 Solving 3 + w = -11.180339887 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 = -11.180339887 + -3 Combine like terms: 3 + -3 = 0 0 + w = -11.180339887 + -3 w = -11.180339887 + -3 Combine like terms: -11.180339887 + -3 = -14.180339887 w = -14.180339887 Simplifying w = -14.180339887Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.180339887, -14.180339887}
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