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Simplifying w2 + -26w = -31 Reorder the terms: -26w + w2 = -31 Solving -26w + w2 = -31 Solving for variable 'w'. Reorder the terms: 31 + -26w + w2 = -31 + 31 Combine like terms: -31 + 31 = 0 31 + -26w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + -26w + -31 + w2 = 0 + -31 Reorder the terms: 31 + -31 + -26w + w2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + -26w + w2 = 0 + -31 -26w + w2 = 0 + -31 Combine like terms: 0 + -31 = -31 -26w + w2 = -31 The w term is -26w. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26w + 169 + w2 = -31 + 169 Reorder the terms: 169 + -26w + w2 = -31 + 169 Combine like terms: -31 + 169 = 138 169 + -26w + w2 = 138 Factor a perfect square on the left side: (w + -13)(w + -13) = 138 Calculate the square root of the right side: 11.747340124 Break this problem into two subproblems by setting (w + -13) equal to 11.747340124 and -11.747340124.Subproblem 1
w + -13 = 11.747340124 Simplifying w + -13 = 11.747340124 Reorder the terms: -13 + w = 11.747340124 Solving -13 + w = 11.747340124 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + w = 11.747340124 + 13 Combine like terms: -13 + 13 = 0 0 + w = 11.747340124 + 13 w = 11.747340124 + 13 Combine like terms: 11.747340124 + 13 = 24.747340124 w = 24.747340124 Simplifying w = 24.747340124Subproblem 2
w + -13 = -11.747340124 Simplifying w + -13 = -11.747340124 Reorder the terms: -13 + w = -11.747340124 Solving -13 + w = -11.747340124 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + w = -11.747340124 + 13 Combine like terms: -13 + 13 = 0 0 + w = -11.747340124 + 13 w = -11.747340124 + 13 Combine like terms: -11.747340124 + 13 = 1.252659876 w = 1.252659876 Simplifying w = 1.252659876Solution
The solution to the problem is based on the solutions from the subproblems. w = {24.747340124, 1.252659876}
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