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Simplifying 2w2 + 13w + 16 + -1w2 + 12w + -36 = 0 Reorder the terms: 16 + -36 + 13w + 12w + 2w2 + -1w2 = 0 Combine like terms: 16 + -36 = -20 -20 + 13w + 12w + 2w2 + -1w2 = 0 Combine like terms: 13w + 12w = 25w -20 + 25w + 2w2 + -1w2 = 0 Combine like terms: 2w2 + -1w2 = 1w2 -20 + 25w + 1w2 = 0 Solving -20 + 25w + 1w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 25w + 20 + w2 = 0 + 20 Reorder the terms: -20 + 20 + 25w + w2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 25w + w2 = 0 + 20 25w + w2 = 0 + 20 Combine like terms: 0 + 20 = 20 25w + w2 = 20 The w term is 25w. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25w + 156.25 + w2 = 20 + 156.25 Reorder the terms: 156.25 + 25w + w2 = 20 + 156.25 Combine like terms: 20 + 156.25 = 176.25 156.25 + 25w + w2 = 176.25 Factor a perfect square on the left side: (w + 12.5)(w + 12.5) = 176.25 Calculate the square root of the right side: 13.275918047 Break this problem into two subproblems by setting (w + 12.5) equal to 13.275918047 and -13.275918047.Subproblem 1
w + 12.5 = 13.275918047 Simplifying w + 12.5 = 13.275918047 Reorder the terms: 12.5 + w = 13.275918047 Solving 12.5 + w = 13.275918047 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + w = 13.275918047 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + w = 13.275918047 + -12.5 w = 13.275918047 + -12.5 Combine like terms: 13.275918047 + -12.5 = 0.775918047 w = 0.775918047 Simplifying w = 0.775918047Subproblem 2
w + 12.5 = -13.275918047 Simplifying w + 12.5 = -13.275918047 Reorder the terms: 12.5 + w = -13.275918047 Solving 12.5 + w = -13.275918047 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + w = -13.275918047 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + w = -13.275918047 + -12.5 w = -13.275918047 + -12.5 Combine like terms: -13.275918047 + -12.5 = -25.775918047 w = -25.775918047 Simplifying w = -25.775918047Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.775918047, -25.775918047}
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