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Simplifying 2w2 + 13w + -259 = 0 Reorder the terms: -259 + 13w + 2w2 = 0 Solving -259 + 13w + 2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -129.5 + 6.5w + w2 = 0 Move the constant term to the right: Add '129.5' to each side of the equation. -129.5 + 6.5w + 129.5 + w2 = 0 + 129.5 Reorder the terms: -129.5 + 129.5 + 6.5w + w2 = 0 + 129.5 Combine like terms: -129.5 + 129.5 = 0.0 0.0 + 6.5w + w2 = 0 + 129.5 6.5w + w2 = 0 + 129.5 Combine like terms: 0 + 129.5 = 129.5 6.5w + w2 = 129.5 The w term is 6.5w. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5w + 10.5625 + w2 = 129.5 + 10.5625 Reorder the terms: 10.5625 + 6.5w + w2 = 129.5 + 10.5625 Combine like terms: 129.5 + 10.5625 = 140.0625 10.5625 + 6.5w + w2 = 140.0625 Factor a perfect square on the left side: (w + 3.25)(w + 3.25) = 140.0625 Calculate the square root of the right side: 11.834800379 Break this problem into two subproblems by setting (w + 3.25) equal to 11.834800379 and -11.834800379.Subproblem 1
w + 3.25 = 11.834800379 Simplifying w + 3.25 = 11.834800379 Reorder the terms: 3.25 + w = 11.834800379 Solving 3.25 + w = 11.834800379 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + w = 11.834800379 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + w = 11.834800379 + -3.25 w = 11.834800379 + -3.25 Combine like terms: 11.834800379 + -3.25 = 8.584800379 w = 8.584800379 Simplifying w = 8.584800379Subproblem 2
w + 3.25 = -11.834800379 Simplifying w + 3.25 = -11.834800379 Reorder the terms: 3.25 + w = -11.834800379 Solving 3.25 + w = -11.834800379 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + w = -11.834800379 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + w = -11.834800379 + -3.25 w = -11.834800379 + -3.25 Combine like terms: -11.834800379 + -3.25 = -15.084800379 w = -15.084800379 Simplifying w = -15.084800379Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.584800379, -15.084800379}
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