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Simplifying w2 + -26w + -42 = 0 Reorder the terms: -42 + -26w + w2 = 0 Solving -42 + -26w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -26w + 42 + w2 = 0 + 42 Reorder the terms: -42 + 42 + -26w + w2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -26w + w2 = 0 + 42 -26w + w2 = 0 + 42 Combine like terms: 0 + 42 = 42 -26w + w2 = 42 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 = 42 + 169 Reorder the terms: 169 + -26w + w2 = 42 + 169 Combine like terms: 42 + 169 = 211 169 + -26w + w2 = 211 Factor a perfect square on the left side: (w + -13)(w + -13) = 211 Calculate the square root of the right side: 14.525839046 Break this problem into two subproblems by setting (w + -13) equal to 14.525839046 and -14.525839046.Subproblem 1
w + -13 = 14.525839046 Simplifying w + -13 = 14.525839046 Reorder the terms: -13 + w = 14.525839046 Solving -13 + w = 14.525839046 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 = 14.525839046 + 13 Combine like terms: -13 + 13 = 0 0 + w = 14.525839046 + 13 w = 14.525839046 + 13 Combine like terms: 14.525839046 + 13 = 27.525839046 w = 27.525839046 Simplifying w = 27.525839046Subproblem 2
w + -13 = -14.525839046 Simplifying w + -13 = -14.525839046 Reorder the terms: -13 + w = -14.525839046 Solving -13 + w = -14.525839046 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 = -14.525839046 + 13 Combine like terms: -13 + 13 = 0 0 + w = -14.525839046 + 13 w = -14.525839046 + 13 Combine like terms: -14.525839046 + 13 = -1.525839046 w = -1.525839046 Simplifying w = -1.525839046Solution
The solution to the problem is based on the solutions from the subproblems. w = {27.525839046, -1.525839046}
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