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Simplifying w(w + 4) = 116 Reorder the terms: w(4 + w) = 116 (4 * w + w * w) = 116 (4w + w2) = 116 Solving 4w + w2 = 116 Solving for variable 'w'. Reorder the terms: -116 + 4w + w2 = 116 + -116 Combine like terms: 116 + -116 = 0 -116 + 4w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '116' to each side of the equation. -116 + 4w + 116 + w2 = 0 + 116 Reorder the terms: -116 + 116 + 4w + w2 = 0 + 116 Combine like terms: -116 + 116 = 0 0 + 4w + w2 = 0 + 116 4w + w2 = 0 + 116 Combine like terms: 0 + 116 = 116 4w + w2 = 116 The w term is 4w. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4w + 4 + w2 = 116 + 4 Reorder the terms: 4 + 4w + w2 = 116 + 4 Combine like terms: 116 + 4 = 120 4 + 4w + w2 = 120 Factor a perfect square on the left side: (w + 2)(w + 2) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (w + 2) equal to 10.95445115 and -10.95445115.Subproblem 1
w + 2 = 10.95445115 Simplifying w + 2 = 10.95445115 Reorder the terms: 2 + w = 10.95445115 Solving 2 + w = 10.95445115 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 10.95445115 + -2 Combine like terms: 2 + -2 = 0 0 + w = 10.95445115 + -2 w = 10.95445115 + -2 Combine like terms: 10.95445115 + -2 = 8.95445115 w = 8.95445115 Simplifying w = 8.95445115Subproblem 2
w + 2 = -10.95445115 Simplifying w + 2 = -10.95445115 Reorder the terms: 2 + w = -10.95445115 Solving 2 + w = -10.95445115 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = -10.95445115 + -2 Combine like terms: 2 + -2 = 0 0 + w = -10.95445115 + -2 w = -10.95445115 + -2 Combine like terms: -10.95445115 + -2 = -12.95445115 w = -12.95445115 Simplifying w = -12.95445115Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.95445115, -12.95445115}
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