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Simplifying 4w2 + -2w = 87 Reorder the terms: -2w + 4w2 = 87 Solving -2w + 4w2 = 87 Solving for variable 'w'. Reorder the terms: -87 + -2w + 4w2 = 87 + -87 Combine like terms: 87 + -87 = 0 -87 + -2w + 4w2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -21.75 + -0.5w + w2 = 0 Move the constant term to the right: Add '21.75' to each side of the equation. -21.75 + -0.5w + 21.75 + w2 = 0 + 21.75 Reorder the terms: -21.75 + 21.75 + -0.5w + w2 = 0 + 21.75 Combine like terms: -21.75 + 21.75 = 0.00 0.00 + -0.5w + w2 = 0 + 21.75 -0.5w + w2 = 0 + 21.75 Combine like terms: 0 + 21.75 = 21.75 -0.5w + w2 = 21.75 The w term is -0.5w. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5w + 0.0625 + w2 = 21.75 + 0.0625 Reorder the terms: 0.0625 + -0.5w + w2 = 21.75 + 0.0625 Combine like terms: 21.75 + 0.0625 = 21.8125 0.0625 + -0.5w + w2 = 21.8125 Factor a perfect square on the left side: (w + -0.25)(w + -0.25) = 21.8125 Calculate the square root of the right side: 4.670385423 Break this problem into two subproblems by setting (w + -0.25) equal to 4.670385423 and -4.670385423.Subproblem 1
w + -0.25 = 4.670385423 Simplifying w + -0.25 = 4.670385423 Reorder the terms: -0.25 + w = 4.670385423 Solving -0.25 + w = 4.670385423 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + w = 4.670385423 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + w = 4.670385423 + 0.25 w = 4.670385423 + 0.25 Combine like terms: 4.670385423 + 0.25 = 4.920385423 w = 4.920385423 Simplifying w = 4.920385423Subproblem 2
w + -0.25 = -4.670385423 Simplifying w + -0.25 = -4.670385423 Reorder the terms: -0.25 + w = -4.670385423 Solving -0.25 + w = -4.670385423 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + w = -4.670385423 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + w = -4.670385423 + 0.25 w = -4.670385423 + 0.25 Combine like terms: -4.670385423 + 0.25 = -4.420385423 w = -4.420385423 Simplifying w = -4.420385423Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.920385423, -4.420385423}
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