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Simplifying w2 + 0.5w + -288 = 0 Reorder the terms: -288 + 0.5w + w2 = 0 Solving -288 + 0.5w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '288' to each side of the equation. -288 + 0.5w + 288 + w2 = 0 + 288 Reorder the terms: -288 + 288 + 0.5w + w2 = 0 + 288 Combine like terms: -288 + 288 = 0 0 + 0.5w + w2 = 0 + 288 0.5w + w2 = 0 + 288 Combine like terms: 0 + 288 = 288 0.5w + w2 = 288 The w term is 0.5w. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5w + 0.0625 + w2 = 288 + 0.0625 Reorder the terms: 0.0625 + 0.5w + w2 = 288 + 0.0625 Combine like terms: 288 + 0.0625 = 288.0625 0.0625 + 0.5w + w2 = 288.0625 Factor a perfect square on the left side: (w + 0.25)(w + 0.25) = 288.0625 Calculate the square root of the right side: 16.972404072 Break this problem into two subproblems by setting (w + 0.25) equal to 16.972404072 and -16.972404072.Subproblem 1
w + 0.25 = 16.972404072 Simplifying w + 0.25 = 16.972404072 Reorder the terms: 0.25 + w = 16.972404072 Solving 0.25 + w = 16.972404072 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + w = 16.972404072 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + w = 16.972404072 + -0.25 w = 16.972404072 + -0.25 Combine like terms: 16.972404072 + -0.25 = 16.722404072 w = 16.722404072 Simplifying w = 16.722404072Subproblem 2
w + 0.25 = -16.972404072 Simplifying w + 0.25 = -16.972404072 Reorder the terms: 0.25 + w = -16.972404072 Solving 0.25 + w = -16.972404072 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + w = -16.972404072 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + w = -16.972404072 + -0.25 w = -16.972404072 + -0.25 Combine like terms: -16.972404072 + -0.25 = -17.222404072 w = -17.222404072 Simplifying w = -17.222404072Solution
The solution to the problem is based on the solutions from the subproblems. w = {16.722404072, -17.222404072}
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