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Simplifying -1w2 + 26w + -148.75 = 0 Reorder the terms: -148.75 + 26w + -1w2 = 0 Solving -148.75 + 26w + -1w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 148.75 + -26w + w2 = 0 Move the constant term to the right: Add '-148.75' to each side of the equation. 148.75 + -26w + -148.75 + w2 = 0 + -148.75 Reorder the terms: 148.75 + -148.75 + -26w + w2 = 0 + -148.75 Combine like terms: 148.75 + -148.75 = 0.00 0.00 + -26w + w2 = 0 + -148.75 -26w + w2 = 0 + -148.75 Combine like terms: 0 + -148.75 = -148.75 -26w + w2 = -148.75 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 = -148.75 + 169 Reorder the terms: 169 + -26w + w2 = -148.75 + 169 Combine like terms: -148.75 + 169 = 20.25 169 + -26w + w2 = 20.25 Factor a perfect square on the left side: (w + -13)(w + -13) = 20.25 Calculate the square root of the right side: 4.5 Break this problem into two subproblems by setting (w + -13) equal to 4.5 and -4.5.Subproblem 1
w + -13 = 4.5 Simplifying w + -13 = 4.5 Reorder the terms: -13 + w = 4.5 Solving -13 + w = 4.5 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 = 4.5 + 13 Combine like terms: -13 + 13 = 0 0 + w = 4.5 + 13 w = 4.5 + 13 Combine like terms: 4.5 + 13 = 17.5 w = 17.5 Simplifying w = 17.5Subproblem 2
w + -13 = -4.5 Simplifying w + -13 = -4.5 Reorder the terms: -13 + w = -4.5 Solving -13 + w = -4.5 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 = -4.5 + 13 Combine like terms: -13 + 13 = 0 0 + w = -4.5 + 13 w = -4.5 + 13 Combine like terms: -4.5 + 13 = 8.5 w = 8.5 Simplifying w = 8.5Solution
The solution to the problem is based on the solutions from the subproblems. w = {17.5, 8.5}
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