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Simplifying 4w2 + -8 = 5w Reorder the terms: -8 + 4w2 = 5w Solving -8 + 4w2 = 5w Solving for variable 'w'. Reorder the terms: -8 + -5w + 4w2 = 5w + -5w Combine like terms: 5w + -5w = 0 -8 + -5w + 4w2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + -1.25w + w2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.25w + 2 + w2 = 0 + 2 Reorder the terms: -2 + 2 + -1.25w + w2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.25w + w2 = 0 + 2 -1.25w + w2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.25w + w2 = 2 The w term is -1.25w. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25w + 0.390625 + w2 = 2 + 0.390625 Reorder the terms: 0.390625 + -1.25w + w2 = 2 + 0.390625 Combine like terms: 2 + 0.390625 = 2.390625 0.390625 + -1.25w + w2 = 2.390625 Factor a perfect square on the left side: (w + -0.625)(w + -0.625) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (w + -0.625) equal to 1.54616461 and -1.54616461.Subproblem 1
w + -0.625 = 1.54616461 Simplifying w + -0.625 = 1.54616461 Reorder the terms: -0.625 + w = 1.54616461 Solving -0.625 + w = 1.54616461 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + w = 1.54616461 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + w = 1.54616461 + 0.625 w = 1.54616461 + 0.625 Combine like terms: 1.54616461 + 0.625 = 2.17116461 w = 2.17116461 Simplifying w = 2.17116461Subproblem 2
w + -0.625 = -1.54616461 Simplifying w + -0.625 = -1.54616461 Reorder the terms: -0.625 + w = -1.54616461 Solving -0.625 + w = -1.54616461 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + w = -1.54616461 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + w = -1.54616461 + 0.625 w = -1.54616461 + 0.625 Combine like terms: -1.54616461 + 0.625 = -0.92116461 w = -0.92116461 Simplifying w = -0.92116461Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.17116461, -0.92116461}
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