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Simplifying 2w + w(w + -10) = 2w + -19 Reorder the terms: 2w + w(-10 + w) = 2w + -19 2w + (-10 * w + w * w) = 2w + -19 2w + (-10w + w2) = 2w + -19 Combine like terms: 2w + -10w = -8w -8w + w2 = 2w + -19 Reorder the terms: -8w + w2 = -19 + 2w Solving -8w + w2 = -19 + 2w Solving for variable 'w'. Reorder the terms: 19 + -8w + -2w + w2 = -19 + 2w + 19 + -2w Combine like terms: -8w + -2w = -10w 19 + -10w + w2 = -19 + 2w + 19 + -2w Reorder the terms: 19 + -10w + w2 = -19 + 19 + 2w + -2w Combine like terms: -19 + 19 = 0 19 + -10w + w2 = 0 + 2w + -2w 19 + -10w + w2 = 2w + -2w Combine like terms: 2w + -2w = 0 19 + -10w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -10w + -19 + w2 = 0 + -19 Reorder the terms: 19 + -19 + -10w + w2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -10w + w2 = 0 + -19 -10w + w2 = 0 + -19 Combine like terms: 0 + -19 = -19 -10w + w2 = -19 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 = -19 + 25 Reorder the terms: 25 + -10w + w2 = -19 + 25 Combine like terms: -19 + 25 = 6 25 + -10w + w2 = 6 Factor a perfect square on the left side: (w + -5)(w + -5) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (w + -5) equal to 2.449489743 and -2.449489743.Subproblem 1
w + -5 = 2.449489743 Simplifying w + -5 = 2.449489743 Reorder the terms: -5 + w = 2.449489743 Solving -5 + w = 2.449489743 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 = 2.449489743 + 5 Combine like terms: -5 + 5 = 0 0 + w = 2.449489743 + 5 w = 2.449489743 + 5 Combine like terms: 2.449489743 + 5 = 7.449489743 w = 7.449489743 Simplifying w = 7.449489743Subproblem 2
w + -5 = -2.449489743 Simplifying w + -5 = -2.449489743 Reorder the terms: -5 + w = -2.449489743 Solving -5 + w = -2.449489743 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 = -2.449489743 + 5 Combine like terms: -5 + 5 = 0 0 + w = -2.449489743 + 5 w = -2.449489743 + 5 Combine like terms: -2.449489743 + 5 = 2.550510257 w = 2.550510257 Simplifying w = 2.550510257Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.449489743, 2.550510257}
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