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Simplifying w2 + -28w = -31 Reorder the terms: -28w + w2 = -31 Solving -28w + w2 = -31 Solving for variable 'w'. Reorder the terms: 31 + -28w + w2 = -31 + 31 Combine like terms: -31 + 31 = 0 31 + -28w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + -28w + -31 + w2 = 0 + -31 Reorder the terms: 31 + -31 + -28w + w2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + -28w + w2 = 0 + -31 -28w + w2 = 0 + -31 Combine like terms: 0 + -31 = -31 -28w + w2 = -31 The w term is -28w. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28w + 196 + w2 = -31 + 196 Reorder the terms: 196 + -28w + w2 = -31 + 196 Combine like terms: -31 + 196 = 165 196 + -28w + w2 = 165 Factor a perfect square on the left side: (w + -14)(w + -14) = 165 Calculate the square root of the right side: 12.845232579 Break this problem into two subproblems by setting (w + -14) equal to 12.845232579 and -12.845232579.Subproblem 1
w + -14 = 12.845232579 Simplifying w + -14 = 12.845232579 Reorder the terms: -14 + w = 12.845232579 Solving -14 + w = 12.845232579 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + w = 12.845232579 + 14 Combine like terms: -14 + 14 = 0 0 + w = 12.845232579 + 14 w = 12.845232579 + 14 Combine like terms: 12.845232579 + 14 = 26.845232579 w = 26.845232579 Simplifying w = 26.845232579Subproblem 2
w + -14 = -12.845232579 Simplifying w + -14 = -12.845232579 Reorder the terms: -14 + w = -12.845232579 Solving -14 + w = -12.845232579 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + w = -12.845232579 + 14 Combine like terms: -14 + 14 = 0 0 + w = -12.845232579 + 14 w = -12.845232579 + 14 Combine like terms: -12.845232579 + 14 = 1.154767421 w = 1.154767421 Simplifying w = 1.154767421Solution
The solution to the problem is based on the solutions from the subproblems. w = {26.845232579, 1.154767421}
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