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Simplifying 5w2 + 26w + -5 = 0 Reorder the terms: -5 + 26w + 5w2 = 0 Solving -5 + 26w + 5w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + 5.2w + w2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 5.2w + 1 + w2 = 0 + 1 Reorder the terms: -1 + 1 + 5.2w + w2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 5.2w + w2 = 0 + 1 5.2w + w2 = 0 + 1 Combine like terms: 0 + 1 = 1 5.2w + w2 = 1 The w term is 5.2w. Take half its coefficient (2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. 5.2w + 6.76 + w2 = 1 + 6.76 Reorder the terms: 6.76 + 5.2w + w2 = 1 + 6.76 Combine like terms: 1 + 6.76 = 7.76 6.76 + 5.2w + w2 = 7.76 Factor a perfect square on the left side: (w + 2.6)(w + 2.6) = 7.76 Calculate the square root of the right side: 2.785677655 Break this problem into two subproblems by setting (w + 2.6) equal to 2.785677655 and -2.785677655.Subproblem 1
w + 2.6 = 2.785677655 Simplifying w + 2.6 = 2.785677655 Reorder the terms: 2.6 + w = 2.785677655 Solving 2.6 + w = 2.785677655 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + w = 2.785677655 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + w = 2.785677655 + -2.6 w = 2.785677655 + -2.6 Combine like terms: 2.785677655 + -2.6 = 0.185677655 w = 0.185677655 Simplifying w = 0.185677655Subproblem 2
w + 2.6 = -2.785677655 Simplifying w + 2.6 = -2.785677655 Reorder the terms: 2.6 + w = -2.785677655 Solving 2.6 + w = -2.785677655 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + w = -2.785677655 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + w = -2.785677655 + -2.6 w = -2.785677655 + -2.6 Combine like terms: -2.785677655 + -2.6 = -5.385677655 w = -5.385677655 Simplifying w = -5.385677655Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.185677655, -5.385677655}
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