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Simplifying 2w2 + -7w + -13 = -10 Reorder the terms: -13 + -7w + 2w2 = -10 Solving -13 + -7w + 2w2 = -10 Solving for variable 'w'. Reorder the terms: -13 + 10 + -7w + 2w2 = -10 + 10 Combine like terms: -13 + 10 = -3 -3 + -7w + 2w2 = -10 + 10 Combine like terms: -10 + 10 = 0 -3 + -7w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -3.5w + w2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -3.5w + 1.5 + w2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -3.5w + w2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -3.5w + w2 = 0 + 1.5 -3.5w + w2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -3.5w + w2 = 1.5 The w term is -3.5w. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5w + 3.0625 + w2 = 1.5 + 3.0625 Reorder the terms: 3.0625 + -3.5w + w2 = 1.5 + 3.0625 Combine like terms: 1.5 + 3.0625 = 4.5625 3.0625 + -3.5w + w2 = 4.5625 Factor a perfect square on the left side: (w + -1.75)(w + -1.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (w + -1.75) equal to 2.136000936 and -2.136000936.Subproblem 1
w + -1.75 = 2.136000936 Simplifying w + -1.75 = 2.136000936 Reorder the terms: -1.75 + w = 2.136000936 Solving -1.75 + w = 2.136000936 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + w = 2.136000936 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + w = 2.136000936 + 1.75 w = 2.136000936 + 1.75 Combine like terms: 2.136000936 + 1.75 = 3.886000936 w = 3.886000936 Simplifying w = 3.886000936Subproblem 2
w + -1.75 = -2.136000936 Simplifying w + -1.75 = -2.136000936 Reorder the terms: -1.75 + w = -2.136000936 Solving -1.75 + w = -2.136000936 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + w = -2.136000936 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + w = -2.136000936 + 1.75 w = -2.136000936 + 1.75 Combine like terms: -2.136000936 + 1.75 = -0.386000936 w = -0.386000936 Simplifying w = -0.386000936Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.886000936, -0.386000936}
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