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Simplifying 5w2 + -36w + 32 = 0 Reorder the terms: 32 + -36w + 5w2 = 0 Solving 32 + -36w + 5w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 6.4 + -7.2w + w2 = 0 Move the constant term to the right: Add '-6.4' to each side of the equation. 6.4 + -7.2w + -6.4 + w2 = 0 + -6.4 Reorder the terms: 6.4 + -6.4 + -7.2w + w2 = 0 + -6.4 Combine like terms: 6.4 + -6.4 = 0.0 0.0 + -7.2w + w2 = 0 + -6.4 -7.2w + w2 = 0 + -6.4 Combine like terms: 0 + -6.4 = -6.4 -7.2w + w2 = -6.4 The w term is -7.2w. Take half its coefficient (-3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. -7.2w + 12.96 + w2 = -6.4 + 12.96 Reorder the terms: 12.96 + -7.2w + w2 = -6.4 + 12.96 Combine like terms: -6.4 + 12.96 = 6.56 12.96 + -7.2w + w2 = 6.56 Factor a perfect square on the left side: (w + -3.6)(w + -3.6) = 6.56 Calculate the square root of the right side: 2.561249695 Break this problem into two subproblems by setting (w + -3.6) equal to 2.561249695 and -2.561249695.Subproblem 1
w + -3.6 = 2.561249695 Simplifying w + -3.6 = 2.561249695 Reorder the terms: -3.6 + w = 2.561249695 Solving -3.6 + w = 2.561249695 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + w = 2.561249695 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + w = 2.561249695 + 3.6 w = 2.561249695 + 3.6 Combine like terms: 2.561249695 + 3.6 = 6.161249695 w = 6.161249695 Simplifying w = 6.161249695Subproblem 2
w + -3.6 = -2.561249695 Simplifying w + -3.6 = -2.561249695 Reorder the terms: -3.6 + w = -2.561249695 Solving -3.6 + w = -2.561249695 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + w = -2.561249695 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + w = -2.561249695 + 3.6 w = -2.561249695 + 3.6 Combine like terms: -2.561249695 + 3.6 = 1.038750305 w = 1.038750305 Simplifying w = 1.038750305Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.161249695, 1.038750305}
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