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Simplifying w2 + 31w + -28 = 0 Reorder the terms: -28 + 31w + w2 = 0 Solving -28 + 31w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 31w + 28 + w2 = 0 + 28 Reorder the terms: -28 + 28 + 31w + w2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 31w + w2 = 0 + 28 31w + w2 = 0 + 28 Combine like terms: 0 + 28 = 28 31w + w2 = 28 The w term is 31w. Take half its coefficient (15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. 31w + 240.25 + w2 = 28 + 240.25 Reorder the terms: 240.25 + 31w + w2 = 28 + 240.25 Combine like terms: 28 + 240.25 = 268.25 240.25 + 31w + w2 = 268.25 Factor a perfect square on the left side: (w + 15.5)(w + 15.5) = 268.25 Calculate the square root of the right side: 16.378339354 Break this problem into two subproblems by setting (w + 15.5) equal to 16.378339354 and -16.378339354.Subproblem 1
w + 15.5 = 16.378339354 Simplifying w + 15.5 = 16.378339354 Reorder the terms: 15.5 + w = 16.378339354 Solving 15.5 + w = 16.378339354 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + w = 16.378339354 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + w = 16.378339354 + -15.5 w = 16.378339354 + -15.5 Combine like terms: 16.378339354 + -15.5 = 0.878339354 w = 0.878339354 Simplifying w = 0.878339354Subproblem 2
w + 15.5 = -16.378339354 Simplifying w + 15.5 = -16.378339354 Reorder the terms: 15.5 + w = -16.378339354 Solving 15.5 + w = -16.378339354 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + w = -16.378339354 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + w = -16.378339354 + -15.5 w = -16.378339354 + -15.5 Combine like terms: -16.378339354 + -15.5 = -31.878339354 w = -31.878339354 Simplifying w = -31.878339354Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.878339354, -31.878339354}
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