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Simplifying 4w2 + -31w + 15 = 0 Reorder the terms: 15 + -31w + 4w2 = 0 Solving 15 + -31w + 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'. 3.75 + -7.75w + w2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -7.75w + -3.75 + w2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -7.75w + w2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -7.75w + w2 = 0 + -3.75 -7.75w + w2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -7.75w + w2 = -3.75 The w term is -7.75w. Take half its coefficient (-3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. -7.75w + 15.015625 + w2 = -3.75 + 15.015625 Reorder the terms: 15.015625 + -7.75w + w2 = -3.75 + 15.015625 Combine like terms: -3.75 + 15.015625 = 11.265625 15.015625 + -7.75w + w2 = 11.265625 Factor a perfect square on the left side: (w + -3.875)(w + -3.875) = 11.265625 Calculate the square root of the right side: 3.356430396 Break this problem into two subproblems by setting (w + -3.875) equal to 3.356430396 and -3.356430396.Subproblem 1
w + -3.875 = 3.356430396 Simplifying w + -3.875 = 3.356430396 Reorder the terms: -3.875 + w = 3.356430396 Solving -3.875 + w = 3.356430396 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + w = 3.356430396 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + w = 3.356430396 + 3.875 w = 3.356430396 + 3.875 Combine like terms: 3.356430396 + 3.875 = 7.231430396 w = 7.231430396 Simplifying w = 7.231430396Subproblem 2
w + -3.875 = -3.356430396 Simplifying w + -3.875 = -3.356430396 Reorder the terms: -3.875 + w = -3.356430396 Solving -3.875 + w = -3.356430396 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + w = -3.356430396 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + w = -3.356430396 + 3.875 w = -3.356430396 + 3.875 Combine like terms: -3.356430396 + 3.875 = 0.518569604 w = 0.518569604 Simplifying w = 0.518569604Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.231430396, 0.518569604}
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