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Simplifying 2w2 + -5w + -122 = 0 Reorder the terms: -122 + -5w + 2w2 = 0 Solving -122 + -5w + 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'. -61 + -2.5w + w2 = 0 Move the constant term to the right: Add '61' to each side of the equation. -61 + -2.5w + 61 + w2 = 0 + 61 Reorder the terms: -61 + 61 + -2.5w + w2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + -2.5w + w2 = 0 + 61 -2.5w + w2 = 0 + 61 Combine like terms: 0 + 61 = 61 -2.5w + w2 = 61 The w term is -2.5w. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5w + 1.5625 + w2 = 61 + 1.5625 Reorder the terms: 1.5625 + -2.5w + w2 = 61 + 1.5625 Combine like terms: 61 + 1.5625 = 62.5625 1.5625 + -2.5w + w2 = 62.5625 Factor a perfect square on the left side: (w + -1.25)(w + -1.25) = 62.5625 Calculate the square root of the right side: 7.90964601 Break this problem into two subproblems by setting (w + -1.25) equal to 7.90964601 and -7.90964601.Subproblem 1
w + -1.25 = 7.90964601 Simplifying w + -1.25 = 7.90964601 Reorder the terms: -1.25 + w = 7.90964601 Solving -1.25 + w = 7.90964601 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + w = 7.90964601 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + w = 7.90964601 + 1.25 w = 7.90964601 + 1.25 Combine like terms: 7.90964601 + 1.25 = 9.15964601 w = 9.15964601 Simplifying w = 9.15964601Subproblem 2
w + -1.25 = -7.90964601 Simplifying w + -1.25 = -7.90964601 Reorder the terms: -1.25 + w = -7.90964601 Solving -1.25 + w = -7.90964601 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + w = -7.90964601 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + w = -7.90964601 + 1.25 w = -7.90964601 + 1.25 Combine like terms: -7.90964601 + 1.25 = -6.65964601 w = -6.65964601 Simplifying w = -6.65964601Solution
The solution to the problem is based on the solutions from the subproblems. w = {9.15964601, -6.65964601}
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