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Simplifying 4w2 + 5w + -60 = 0 Reorder the terms: -60 + 5w + 4w2 = 0 Solving -60 + 5w + 4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -15 + 1.25w + w2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 1.25w + 15 + w2 = 0 + 15 Reorder the terms: -15 + 15 + 1.25w + w2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 1.25w + w2 = 0 + 15 1.25w + w2 = 0 + 15 Combine like terms: 0 + 15 = 15 1.25w + w2 = 15 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 = 15 + 0.390625 Reorder the terms: 0.390625 + 1.25w + w2 = 15 + 0.390625 Combine like terms: 15 + 0.390625 = 15.390625 0.390625 + 1.25w + w2 = 15.390625 Factor a perfect square on the left side: (w + 0.625)(w + 0.625) = 15.390625 Calculate the square root of the right side: 3.923088707 Break this problem into two subproblems by setting (w + 0.625) equal to 3.923088707 and -3.923088707.Subproblem 1
w + 0.625 = 3.923088707 Simplifying w + 0.625 = 3.923088707 Reorder the terms: 0.625 + w = 3.923088707 Solving 0.625 + w = 3.923088707 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 = 3.923088707 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + w = 3.923088707 + -0.625 w = 3.923088707 + -0.625 Combine like terms: 3.923088707 + -0.625 = 3.298088707 w = 3.298088707 Simplifying w = 3.298088707Subproblem 2
w + 0.625 = -3.923088707 Simplifying w + 0.625 = -3.923088707 Reorder the terms: 0.625 + w = -3.923088707 Solving 0.625 + w = -3.923088707 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 = -3.923088707 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + w = -3.923088707 + -0.625 w = -3.923088707 + -0.625 Combine like terms: -3.923088707 + -0.625 = -4.548088707 w = -4.548088707 Simplifying w = -4.548088707Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.298088707, -4.548088707}
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