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Simplifying w2 + -50w + 500 = 0 Reorder the terms: 500 + -50w + w2 = 0 Solving 500 + -50w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-500' to each side of the equation. 500 + -50w + -500 + w2 = 0 + -500 Reorder the terms: 500 + -500 + -50w + w2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -50w + w2 = 0 + -500 -50w + w2 = 0 + -500 Combine like terms: 0 + -500 = -500 -50w + w2 = -500 The w term is -50w. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50w + 625 + w2 = -500 + 625 Reorder the terms: 625 + -50w + w2 = -500 + 625 Combine like terms: -500 + 625 = 125 625 + -50w + w2 = 125 Factor a perfect square on the left side: (w + -25)(w + -25) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (w + -25) equal to 11.180339887 and -11.180339887.Subproblem 1
w + -25 = 11.180339887 Simplifying w + -25 = 11.180339887 Reorder the terms: -25 + w = 11.180339887 Solving -25 + w = 11.180339887 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + w = 11.180339887 + 25 Combine like terms: -25 + 25 = 0 0 + w = 11.180339887 + 25 w = 11.180339887 + 25 Combine like terms: 11.180339887 + 25 = 36.180339887 w = 36.180339887 Simplifying w = 36.180339887Subproblem 2
w + -25 = -11.180339887 Simplifying w + -25 = -11.180339887 Reorder the terms: -25 + w = -11.180339887 Solving -25 + w = -11.180339887 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + w = -11.180339887 + 25 Combine like terms: -25 + 25 = 0 0 + w = -11.180339887 + 25 w = -11.180339887 + 25 Combine like terms: -11.180339887 + 25 = 13.819660113 w = 13.819660113 Simplifying w = 13.819660113Solution
The solution to the problem is based on the solutions from the subproblems. w = {36.180339887, 13.819660113}
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