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Simplifying w2 + -26w = -45 Reorder the terms: -26w + w2 = -45 Solving -26w + w2 = -45 Solving for variable 'w'. Reorder the terms: 45 + -26w + w2 = -45 + 45 Combine like terms: -45 + 45 = 0 45 + -26w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + -26w + -45 + w2 = 0 + -45 Reorder the terms: 45 + -45 + -26w + w2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -26w + w2 = 0 + -45 -26w + w2 = 0 + -45 Combine like terms: 0 + -45 = -45 -26w + w2 = -45 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 = -45 + 169 Reorder the terms: 169 + -26w + w2 = -45 + 169 Combine like terms: -45 + 169 = 124 169 + -26w + w2 = 124 Factor a perfect square on the left side: (w + -13)(w + -13) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (w + -13) equal to 11.135528726 and -11.135528726.Subproblem 1
w + -13 = 11.135528726 Simplifying w + -13 = 11.135528726 Reorder the terms: -13 + w = 11.135528726 Solving -13 + w = 11.135528726 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 = 11.135528726 + 13 Combine like terms: -13 + 13 = 0 0 + w = 11.135528726 + 13 w = 11.135528726 + 13 Combine like terms: 11.135528726 + 13 = 24.135528726 w = 24.135528726 Simplifying w = 24.135528726Subproblem 2
w + -13 = -11.135528726 Simplifying w + -13 = -11.135528726 Reorder the terms: -13 + w = -11.135528726 Solving -13 + w = -11.135528726 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 = -11.135528726 + 13 Combine like terms: -13 + 13 = 0 0 + w = -11.135528726 + 13 w = -11.135528726 + 13 Combine like terms: -11.135528726 + 13 = 1.864471274 w = 1.864471274 Simplifying w = 1.864471274Solution
The solution to the problem is based on the solutions from the subproblems. w = {24.135528726, 1.864471274}
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