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Simplifying (w + -10)(w + -10) + -27 = 0 Reorder the terms: (-10 + w)(w + -10) + -27 = 0 Reorder the terms: (-10 + w)(-10 + w) + -27 = 0 Multiply (-10 + w) * (-10 + w) (-10(-10 + w) + w(-10 + w)) + -27 = 0 ((-10 * -10 + w * -10) + w(-10 + w)) + -27 = 0 ((100 + -10w) + w(-10 + w)) + -27 = 0 (100 + -10w + (-10 * w + w * w)) + -27 = 0 (100 + -10w + (-10w + w2)) + -27 = 0 Combine like terms: -10w + -10w = -20w (100 + -20w + w2) + -27 = 0 Reorder the terms: 100 + -27 + -20w + w2 = 0 Combine like terms: 100 + -27 = 73 73 + -20w + w2 = 0 Solving 73 + -20w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-73' to each side of the equation. 73 + -20w + -73 + w2 = 0 + -73 Reorder the terms: 73 + -73 + -20w + w2 = 0 + -73 Combine like terms: 73 + -73 = 0 0 + -20w + w2 = 0 + -73 -20w + w2 = 0 + -73 Combine like terms: 0 + -73 = -73 -20w + w2 = -73 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 = -73 + 100 Reorder the terms: 100 + -20w + w2 = -73 + 100 Combine like terms: -73 + 100 = 27 100 + -20w + w2 = 27 Factor a perfect square on the left side: (w + -10)(w + -10) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (w + -10) equal to 5.196152423 and -5.196152423.Subproblem 1
w + -10 = 5.196152423 Simplifying w + -10 = 5.196152423 Reorder the terms: -10 + w = 5.196152423 Solving -10 + w = 5.196152423 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 = 5.196152423 + 10 Combine like terms: -10 + 10 = 0 0 + w = 5.196152423 + 10 w = 5.196152423 + 10 Combine like terms: 5.196152423 + 10 = 15.196152423 w = 15.196152423 Simplifying w = 15.196152423Subproblem 2
w + -10 = -5.196152423 Simplifying w + -10 = -5.196152423 Reorder the terms: -10 + w = -5.196152423 Solving -10 + w = -5.196152423 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 = -5.196152423 + 10 Combine like terms: -10 + 10 = 0 0 + w = -5.196152423 + 10 w = -5.196152423 + 10 Combine like terms: -5.196152423 + 10 = 4.803847577 w = 4.803847577 Simplifying w = 4.803847577Solution
The solution to the problem is based on the solutions from the subproblems. w = {15.196152423, 4.803847577}
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