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Simplifying 2w2 + -7w + -494 = 0 Reorder the terms: -494 + -7w + 2w2 = 0 Solving -494 + -7w + 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'. -247 + -3.5w + w2 = 0 Move the constant term to the right: Add '247' to each side of the equation. -247 + -3.5w + 247 + w2 = 0 + 247 Reorder the terms: -247 + 247 + -3.5w + w2 = 0 + 247 Combine like terms: -247 + 247 = 0 0 + -3.5w + w2 = 0 + 247 -3.5w + w2 = 0 + 247 Combine like terms: 0 + 247 = 247 -3.5w + w2 = 247 The w term is -3.5w. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5w + 3.0625 + w2 = 247 + 3.0625 Reorder the terms: 3.0625 + -3.5w + w2 = 247 + 3.0625 Combine like terms: 247 + 3.0625 = 250.0625 3.0625 + -3.5w + w2 = 250.0625 Factor a perfect square on the left side: (w + -1.75)(w + -1.75) = 250.0625 Calculate the square root of the right side: 15.813364601 Break this problem into two subproblems by setting (w + -1.75) equal to 15.813364601 and -15.813364601.Subproblem 1
w + -1.75 = 15.813364601 Simplifying w + -1.75 = 15.813364601 Reorder the terms: -1.75 + w = 15.813364601 Solving -1.75 + w = 15.813364601 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + w = 15.813364601 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + w = 15.813364601 + 1.75 w = 15.813364601 + 1.75 Combine like terms: 15.813364601 + 1.75 = 17.563364601 w = 17.563364601 Simplifying w = 17.563364601Subproblem 2
w + -1.75 = -15.813364601 Simplifying w + -1.75 = -15.813364601 Reorder the terms: -1.75 + w = -15.813364601 Solving -1.75 + w = -15.813364601 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + w = -15.813364601 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + w = -15.813364601 + 1.75 w = -15.813364601 + 1.75 Combine like terms: -15.813364601 + 1.75 = -14.063364601 w = -14.063364601 Simplifying w = -14.063364601Solution
The solution to the problem is based on the solutions from the subproblems. w = {17.563364601, -14.063364601}
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