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Simplifying (w + 10)(w + 10) + -45 = 0 Reorder the terms: (10 + w)(w + 10) + -45 = 0 Reorder the terms: (10 + w)(10 + w) + -45 = 0 Multiply (10 + w) * (10 + w) (10(10 + w) + w(10 + w)) + -45 = 0 ((10 * 10 + w * 10) + w(10 + w)) + -45 = 0 ((100 + 10w) + w(10 + w)) + -45 = 0 (100 + 10w + (10 * w + w * w)) + -45 = 0 (100 + 10w + (10w + w2)) + -45 = 0 Combine like terms: 10w + 10w = 20w (100 + 20w + w2) + -45 = 0 Reorder the terms: 100 + -45 + 20w + w2 = 0 Combine like terms: 100 + -45 = 55 55 + 20w + w2 = 0 Solving 55 + 20w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-55' to each side of the equation. 55 + 20w + -55 + w2 = 0 + -55 Reorder the terms: 55 + -55 + 20w + w2 = 0 + -55 Combine like terms: 55 + -55 = 0 0 + 20w + w2 = 0 + -55 20w + w2 = 0 + -55 Combine like terms: 0 + -55 = -55 20w + w2 = -55 The w term is 20w. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20w + 100 + w2 = -55 + 100 Reorder the terms: 100 + 20w + w2 = -55 + 100 Combine like terms: -55 + 100 = 45 100 + 20w + w2 = 45 Factor a perfect square on the left side: (w + 10)(w + 10) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (w + 10) equal to 6.708203933 and -6.708203933.Subproblem 1
w + 10 = 6.708203933 Simplifying w + 10 = 6.708203933 Reorder the terms: 10 + w = 6.708203933 Solving 10 + w = 6.708203933 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + w = 6.708203933 + -10 Combine like terms: 10 + -10 = 0 0 + w = 6.708203933 + -10 w = 6.708203933 + -10 Combine like terms: 6.708203933 + -10 = -3.291796067 w = -3.291796067 Simplifying w = -3.291796067Subproblem 2
w + 10 = -6.708203933 Simplifying w + 10 = -6.708203933 Reorder the terms: 10 + w = -6.708203933 Solving 10 + w = -6.708203933 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + w = -6.708203933 + -10 Combine like terms: 10 + -10 = 0 0 + w = -6.708203933 + -10 w = -6.708203933 + -10 Combine like terms: -6.708203933 + -10 = -16.708203933 w = -16.708203933 Simplifying w = -16.708203933Solution
The solution to the problem is based on the solutions from the subproblems. w = {-3.291796067, -16.708203933}
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