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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 = 200 169 + -26w + w2 = 200 Factor a perfect square on the left side: (w + -13)(w + -13) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (w + -13) equal to 14.142135624 and -14.142135624.Subproblem 1
w + -13 = 14.142135624 Simplifying w + -13 = 14.142135624 Reorder the terms: -13 + w = 14.142135624 Solving -13 + w = 14.142135624 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 = 14.142135624 + 13 Combine like terms: -13 + 13 = 0 0 + w = 14.142135624 + 13 w = 14.142135624 + 13 Combine like terms: 14.142135624 + 13 = 27.142135624 w = 27.142135624 Simplifying w = 27.142135624Subproblem 2
w + -13 = -14.142135624 Simplifying w + -13 = -14.142135624 Reorder the terms: -13 + w = -14.142135624 Solving -13 + w = -14.142135624 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 = -14.142135624 + 13 Combine like terms: -13 + 13 = 0 0 + w = -14.142135624 + 13 w = -14.142135624 + 13 Combine like terms: -14.142135624 + 13 = -1.142135624 w = -1.142135624 Simplifying w = -1.142135624Solution
The solution to the problem is based on the solutions from the subproblems. w = {27.142135624, -1.142135624}
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