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Simplifying 0 = 9w2 + -1w + -1080 Reorder the terms: 0 = -1080 + -1w + 9w2 Solving 0 = -1080 + -1w + 9w2 Solving for variable 'w'. Combine like terms: 0 + 1080 = 1080 1080 + w + -9w2 = -1080 + -1w + 9w2 + 1080 + w + -9w2 Reorder the terms: 1080 + w + -9w2 = -1080 + 1080 + -1w + w + 9w2 + -9w2 Combine like terms: -1080 + 1080 = 0 1080 + w + -9w2 = 0 + -1w + w + 9w2 + -9w2 1080 + w + -9w2 = -1w + w + 9w2 + -9w2 Combine like terms: -1w + w = 0 1080 + w + -9w2 = 0 + 9w2 + -9w2 1080 + w + -9w2 = 9w2 + -9w2 Combine like terms: 9w2 + -9w2 = 0 1080 + w + -9w2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -120 + -0.1111111111w + w2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + -0.1111111111w + 120 + w2 = 0 + 120 Reorder the terms: -120 + 120 + -0.1111111111w + w2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -0.1111111111w + w2 = 0 + 120 -0.1111111111w + w2 = 0 + 120 Combine like terms: 0 + 120 = 120 -0.1111111111w + w2 = 120 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.1111111111w + 0.25 + w2 = 120 + 0.25 Reorder the terms: 0.25 + -0.1111111111w + w2 = 120 + 0.25 Combine like terms: 120 + 0.25 = 120.25 0.25 + -0.1111111111w + w2 = 120.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (w + 0.5) equal to 10.9658561 and -10.9658561.Subproblem 1
w + 0.5 = 10.9658561 Simplifying w + 0.5 = 10.9658561 Reorder the terms: 0.5 + w = 10.9658561 Solving 0.5 + w = 10.9658561 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 10.9658561 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 10.9658561 + -0.5 w = 10.9658561 + -0.5 Combine like terms: 10.9658561 + -0.5 = 10.4658561 w = 10.4658561 Simplifying w = 10.4658561Subproblem 2
w + 0.5 = -10.9658561 Simplifying w + 0.5 = -10.9658561 Reorder the terms: 0.5 + w = -10.9658561 Solving 0.5 + w = -10.9658561 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -10.9658561 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -10.9658561 + -0.5 w = -10.9658561 + -0.5 Combine like terms: -10.9658561 + -0.5 = -11.4658561 w = -11.4658561 Simplifying w = -11.4658561Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.4658561, -11.4658561}
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