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Simplifying w2 + 3w + -588 = 0 Reorder the terms: -588 + 3w + w2 = 0 Solving -588 + 3w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '588' to each side of the equation. -588 + 3w + 588 + w2 = 0 + 588 Reorder the terms: -588 + 588 + 3w + w2 = 0 + 588 Combine like terms: -588 + 588 = 0 0 + 3w + w2 = 0 + 588 3w + w2 = 0 + 588 Combine like terms: 0 + 588 = 588 3w + w2 = 588 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = 588 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 588 + 2.25 Combine like terms: 588 + 2.25 = 590.25 2.25 + 3w + w2 = 590.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 590.25 Calculate the square root of the right side: 24.295061227 Break this problem into two subproblems by setting (w + 1.5) equal to 24.295061227 and -24.295061227.Subproblem 1
w + 1.5 = 24.295061227 Simplifying w + 1.5 = 24.295061227 Reorder the terms: 1.5 + w = 24.295061227 Solving 1.5 + w = 24.295061227 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 24.295061227 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 24.295061227 + -1.5 w = 24.295061227 + -1.5 Combine like terms: 24.295061227 + -1.5 = 22.795061227 w = 22.795061227 Simplifying w = 22.795061227Subproblem 2
w + 1.5 = -24.295061227 Simplifying w + 1.5 = -24.295061227 Reorder the terms: 1.5 + w = -24.295061227 Solving 1.5 + w = -24.295061227 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -24.295061227 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -24.295061227 + -1.5 w = -24.295061227 + -1.5 Combine like terms: -24.295061227 + -1.5 = -25.795061227 w = -25.795061227 Simplifying w = -25.795061227Solution
The solution to the problem is based on the solutions from the subproblems. w = {22.795061227, -25.795061227}
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