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Simplifying w2 + 4w + -88 = 0 Reorder the terms: -88 + 4w + w2 = 0 Solving -88 + 4w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + 4w + 88 + w2 = 0 + 88 Reorder the terms: -88 + 88 + 4w + w2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + 4w + w2 = 0 + 88 4w + w2 = 0 + 88 Combine like terms: 0 + 88 = 88 4w + w2 = 88 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 = 88 + 4 Reorder the terms: 4 + 4w + w2 = 88 + 4 Combine like terms: 88 + 4 = 92 4 + 4w + w2 = 92 Factor a perfect square on the left side: (w + 2)(w + 2) = 92 Calculate the square root of the right side: 9.591663047 Break this problem into two subproblems by setting (w + 2) equal to 9.591663047 and -9.591663047.Subproblem 1
w + 2 = 9.591663047 Simplifying w + 2 = 9.591663047 Reorder the terms: 2 + w = 9.591663047 Solving 2 + w = 9.591663047 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 = 9.591663047 + -2 Combine like terms: 2 + -2 = 0 0 + w = 9.591663047 + -2 w = 9.591663047 + -2 Combine like terms: 9.591663047 + -2 = 7.591663047 w = 7.591663047 Simplifying w = 7.591663047Subproblem 2
w + 2 = -9.591663047 Simplifying w + 2 = -9.591663047 Reorder the terms: 2 + w = -9.591663047 Solving 2 + w = -9.591663047 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 = -9.591663047 + -2 Combine like terms: 2 + -2 = 0 0 + w = -9.591663047 + -2 w = -9.591663047 + -2 Combine like terms: -9.591663047 + -2 = -11.591663047 w = -11.591663047 Simplifying w = -11.591663047Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.591663047, -11.591663047}
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