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Simplifying w2 + 49 + -2w2 + -23w + 63 = 0 Reorder the terms: 49 + 63 + -23w + w2 + -2w2 = 0 Combine like terms: 49 + 63 = 112 112 + -23w + w2 + -2w2 = 0 Combine like terms: w2 + -2w2 = -1w2 112 + -23w + -1w2 = 0 Solving 112 + -23w + -1w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -112 + 23w + w2 = 0 Move the constant term to the right: Add '112' to each side of the equation. -112 + 23w + 112 + w2 = 0 + 112 Reorder the terms: -112 + 112 + 23w + w2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + 23w + w2 = 0 + 112 23w + w2 = 0 + 112 Combine like terms: 0 + 112 = 112 23w + w2 = 112 The w term is 23w. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23w + 132.25 + w2 = 112 + 132.25 Reorder the terms: 132.25 + 23w + w2 = 112 + 132.25 Combine like terms: 112 + 132.25 = 244.25 132.25 + 23w + w2 = 244.25 Factor a perfect square on the left side: (w + 11.5)(w + 11.5) = 244.25 Calculate the square root of the right side: 15.628499608 Break this problem into two subproblems by setting (w + 11.5) equal to 15.628499608 and -15.628499608.Subproblem 1
w + 11.5 = 15.628499608 Simplifying w + 11.5 = 15.628499608 Reorder the terms: 11.5 + w = 15.628499608 Solving 11.5 + w = 15.628499608 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + w = 15.628499608 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + w = 15.628499608 + -11.5 w = 15.628499608 + -11.5 Combine like terms: 15.628499608 + -11.5 = 4.128499608 w = 4.128499608 Simplifying w = 4.128499608Subproblem 2
w + 11.5 = -15.628499608 Simplifying w + 11.5 = -15.628499608 Reorder the terms: 11.5 + w = -15.628499608 Solving 11.5 + w = -15.628499608 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + w = -15.628499608 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + w = -15.628499608 + -11.5 w = -15.628499608 + -11.5 Combine like terms: -15.628499608 + -11.5 = -27.128499608 w = -27.128499608 Simplifying w = -27.128499608Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.128499608, -27.128499608}
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