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Simplifying 2w2 + 9w + -8 = 0 Reorder the terms: -8 + 9w + 2w2 = 0 Solving -8 + 9w + 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'. -4 + 4.5w + w2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 4.5w + 4 + w2 = 0 + 4 Reorder the terms: -4 + 4 + 4.5w + w2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4.5w + w2 = 0 + 4 4.5w + w2 = 0 + 4 Combine like terms: 0 + 4 = 4 4.5w + w2 = 4 The w term is 4.5w. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5w + 5.0625 + w2 = 4 + 5.0625 Reorder the terms: 5.0625 + 4.5w + w2 = 4 + 5.0625 Combine like terms: 4 + 5.0625 = 9.0625 5.0625 + 4.5w + w2 = 9.0625 Factor a perfect square on the left side: (w + 2.25)(w + 2.25) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (w + 2.25) equal to 3.010398645 and -3.010398645.Subproblem 1
w + 2.25 = 3.010398645 Simplifying w + 2.25 = 3.010398645 Reorder the terms: 2.25 + w = 3.010398645 Solving 2.25 + w = 3.010398645 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + w = 3.010398645 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + w = 3.010398645 + -2.25 w = 3.010398645 + -2.25 Combine like terms: 3.010398645 + -2.25 = 0.760398645 w = 0.760398645 Simplifying w = 0.760398645Subproblem 2
w + 2.25 = -3.010398645 Simplifying w + 2.25 = -3.010398645 Reorder the terms: 2.25 + w = -3.010398645 Solving 2.25 + w = -3.010398645 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + w = -3.010398645 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + w = -3.010398645 + -2.25 w = -3.010398645 + -2.25 Combine like terms: -3.010398645 + -2.25 = -5.260398645 w = -5.260398645 Simplifying w = -5.260398645Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.760398645, -5.260398645}
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