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Simplifying 110 = w2 + 6w + -110 Reorder the terms: 110 = -110 + 6w + w2 Solving 110 = -110 + 6w + w2 Solving for variable 'w'. Combine like terms: 110 + 110 = 220 220 + -6w + -1w2 = -110 + 6w + w2 + 110 + -6w + -1w2 Reorder the terms: 220 + -6w + -1w2 = -110 + 110 + 6w + -6w + w2 + -1w2 Combine like terms: -110 + 110 = 0 220 + -6w + -1w2 = 0 + 6w + -6w + w2 + -1w2 220 + -6w + -1w2 = 6w + -6w + w2 + -1w2 Combine like terms: 6w + -6w = 0 220 + -6w + -1w2 = 0 + w2 + -1w2 220 + -6w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 220 + -6w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -220 + 6w + w2 = 0 Move the constant term to the right: Add '220' to each side of the equation. -220 + 6w + 220 + w2 = 0 + 220 Reorder the terms: -220 + 220 + 6w + w2 = 0 + 220 Combine like terms: -220 + 220 = 0 0 + 6w + w2 = 0 + 220 6w + w2 = 0 + 220 Combine like terms: 0 + 220 = 220 6w + w2 = 220 The w term is 6w. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6w + 9 + w2 = 220 + 9 Reorder the terms: 9 + 6w + w2 = 220 + 9 Combine like terms: 220 + 9 = 229 9 + 6w + w2 = 229 Factor a perfect square on the left side: (w + 3)(w + 3) = 229 Calculate the square root of the right side: 15.13274595 Break this problem into two subproblems by setting (w + 3) equal to 15.13274595 and -15.13274595.Subproblem 1
w + 3 = 15.13274595 Simplifying w + 3 = 15.13274595 Reorder the terms: 3 + w = 15.13274595 Solving 3 + w = 15.13274595 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 15.13274595 + -3 Combine like terms: 3 + -3 = 0 0 + w = 15.13274595 + -3 w = 15.13274595 + -3 Combine like terms: 15.13274595 + -3 = 12.13274595 w = 12.13274595 Simplifying w = 12.13274595Subproblem 2
w + 3 = -15.13274595 Simplifying w + 3 = -15.13274595 Reorder the terms: 3 + w = -15.13274595 Solving 3 + w = -15.13274595 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = -15.13274595 + -3 Combine like terms: 3 + -3 = 0 0 + w = -15.13274595 + -3 w = -15.13274595 + -3 Combine like terms: -15.13274595 + -3 = -18.13274595 w = -18.13274595 Simplifying w = -18.13274595Solution
The solution to the problem is based on the solutions from the subproblems. w = {12.13274595, -18.13274595}
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