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Simplifying w2 + 10w = -3 Reorder the terms: 10w + w2 = -3 Solving 10w + w2 = -3 Solving for variable 'w'. Reorder the terms: 3 + 10w + w2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + 10w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 10w + -3 + w2 = 0 + -3 Reorder the terms: 3 + -3 + 10w + w2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 10w + w2 = 0 + -3 10w + w2 = 0 + -3 Combine like terms: 0 + -3 = -3 10w + w2 = -3 The w term is 10w. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10w + 25 + w2 = -3 + 25 Reorder the terms: 25 + 10w + w2 = -3 + 25 Combine like terms: -3 + 25 = 22 25 + 10w + w2 = 22 Factor a perfect square on the left side: (w + 5)(w + 5) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (w + 5) equal to 4.69041576 and -4.69041576.Subproblem 1
w + 5 = 4.69041576 Simplifying w + 5 = 4.69041576 Reorder the terms: 5 + w = 4.69041576 Solving 5 + w = 4.69041576 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = 4.69041576 + -5 Combine like terms: 5 + -5 = 0 0 + w = 4.69041576 + -5 w = 4.69041576 + -5 Combine like terms: 4.69041576 + -5 = -0.30958424 w = -0.30958424 Simplifying w = -0.30958424Subproblem 2
w + 5 = -4.69041576 Simplifying w + 5 = -4.69041576 Reorder the terms: 5 + w = -4.69041576 Solving 5 + w = -4.69041576 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = -4.69041576 + -5 Combine like terms: 5 + -5 = 0 0 + w = -4.69041576 + -5 w = -4.69041576 + -5 Combine like terms: -4.69041576 + -5 = -9.69041576 w = -9.69041576 Simplifying w = -9.69041576Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.30958424, -9.69041576}
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