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Simplifying 3w2 + -9w + -26 = 0 Reorder the terms: -26 + -9w + 3w2 = 0 Solving -26 + -9w + 3w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8.666666667 + -3w + w2 = 0 Move the constant term to the right: Add '8.666666667' to each side of the equation. -8.666666667 + -3w + 8.666666667 + w2 = 0 + 8.666666667 Reorder the terms: -8.666666667 + 8.666666667 + -3w + w2 = 0 + 8.666666667 Combine like terms: -8.666666667 + 8.666666667 = 0.000000000 0.000000000 + -3w + w2 = 0 + 8.666666667 -3w + w2 = 0 + 8.666666667 Combine like terms: 0 + 8.666666667 = 8.666666667 -3w + w2 = 8.666666667 The w term is -3w. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3w + 2.25 + w2 = 8.666666667 + 2.25 Reorder the terms: 2.25 + -3w + w2 = 8.666666667 + 2.25 Combine like terms: 8.666666667 + 2.25 = 10.916666667 2.25 + -3w + w2 = 10.916666667 Factor a perfect square on the left side: (w + -1.5)(w + -1.5) = 10.916666667 Calculate the square root of the right side: 3.304037934 Break this problem into two subproblems by setting (w + -1.5) equal to 3.304037934 and -3.304037934.Subproblem 1
w + -1.5 = 3.304037934 Simplifying w + -1.5 = 3.304037934 Reorder the terms: -1.5 + w = 3.304037934 Solving -1.5 + w = 3.304037934 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + w = 3.304037934 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + w = 3.304037934 + 1.5 w = 3.304037934 + 1.5 Combine like terms: 3.304037934 + 1.5 = 4.804037934 w = 4.804037934 Simplifying w = 4.804037934Subproblem 2
w + -1.5 = -3.304037934 Simplifying w + -1.5 = -3.304037934 Reorder the terms: -1.5 + w = -3.304037934 Solving -1.5 + w = -3.304037934 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + w = -3.304037934 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + w = -3.304037934 + 1.5 w = -3.304037934 + 1.5 Combine like terms: -3.304037934 + 1.5 = -1.804037934 w = -1.804037934 Simplifying w = -1.804037934Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.804037934, -1.804037934}
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