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Simplifying w2 + -1w + -300 = 0 Reorder the terms: -300 + -1w + w2 = 0 Solving -300 + -1w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + -1w + 300 + w2 = 0 + 300 Reorder the terms: -300 + 300 + -1w + w2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + -1w + w2 = 0 + 300 -1w + w2 = 0 + 300 Combine like terms: 0 + 300 = 300 -1w + w2 = 300 The w term is -1w. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1w + 0.25 + w2 = 300 + 0.25 Reorder the terms: 0.25 + -1w + w2 = 300 + 0.25 Combine like terms: 300 + 0.25 = 300.25 0.25 + -1w + w2 = 300.25 Factor a perfect square on the left side: (w + -0.5)(w + -0.5) = 300.25 Calculate the square root of the right side: 17.327723451 Break this problem into two subproblems by setting (w + -0.5) equal to 17.327723451 and -17.327723451.Subproblem 1
w + -0.5 = 17.327723451 Simplifying w + -0.5 = 17.327723451 Reorder the terms: -0.5 + w = 17.327723451 Solving -0.5 + w = 17.327723451 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + w = 17.327723451 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + w = 17.327723451 + 0.5 w = 17.327723451 + 0.5 Combine like terms: 17.327723451 + 0.5 = 17.827723451 w = 17.827723451 Simplifying w = 17.827723451Subproblem 2
w + -0.5 = -17.327723451 Simplifying w + -0.5 = -17.327723451 Reorder the terms: -0.5 + w = -17.327723451 Solving -0.5 + w = -17.327723451 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + w = -17.327723451 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + w = -17.327723451 + 0.5 w = -17.327723451 + 0.5 Combine like terms: -17.327723451 + 0.5 = -16.827723451 w = -16.827723451 Simplifying w = -16.827723451Solution
The solution to the problem is based on the solutions from the subproblems. w = {17.827723451, -16.827723451}
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