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Simplifying W2 + 125W + -264 = 0 Reorder the terms: -264 + 125W + W2 = 0 Solving -264 + 125W + W2 = 0 Solving for variable 'W'. Begin completing the square. Move the constant term to the right: Add '264' to each side of the equation. -264 + 125W + 264 + W2 = 0 + 264 Reorder the terms: -264 + 264 + 125W + W2 = 0 + 264 Combine like terms: -264 + 264 = 0 0 + 125W + W2 = 0 + 264 125W + W2 = 0 + 264 Combine like terms: 0 + 264 = 264 125W + W2 = 264 The W term is 125W. Take half its coefficient (62.5). Square it (3906.25) and add it to both sides. Add '3906.25' to each side of the equation. 125W + 3906.25 + W2 = 264 + 3906.25 Reorder the terms: 3906.25 + 125W + W2 = 264 + 3906.25 Combine like terms: 264 + 3906.25 = 4170.25 3906.25 + 125W + W2 = 4170.25 Factor a perfect square on the left side: (W + 62.5)(W + 62.5) = 4170.25 Calculate the square root of the right side: 64.577472852 Break this problem into two subproblems by setting (W + 62.5) equal to 64.577472852 and -64.577472852.Subproblem 1
W + 62.5 = 64.577472852 Simplifying W + 62.5 = 64.577472852 Reorder the terms: 62.5 + W = 64.577472852 Solving 62.5 + W = 64.577472852 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '-62.5' to each side of the equation. 62.5 + -62.5 + W = 64.577472852 + -62.5 Combine like terms: 62.5 + -62.5 = 0.0 0.0 + W = 64.577472852 + -62.5 W = 64.577472852 + -62.5 Combine like terms: 64.577472852 + -62.5 = 2.077472852 W = 2.077472852 Simplifying W = 2.077472852Subproblem 2
W + 62.5 = -64.577472852 Simplifying W + 62.5 = -64.577472852 Reorder the terms: 62.5 + W = -64.577472852 Solving 62.5 + W = -64.577472852 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '-62.5' to each side of the equation. 62.5 + -62.5 + W = -64.577472852 + -62.5 Combine like terms: 62.5 + -62.5 = 0.0 0.0 + W = -64.577472852 + -62.5 W = -64.577472852 + -62.5 Combine like terms: -64.577472852 + -62.5 = -127.077472852 W = -127.077472852 Simplifying W = -127.077472852Solution
The solution to the problem is based on the solutions from the subproblems. W = {2.077472852, -127.077472852}
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