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Simplifying 2w2 + 9w + -138 = 0 Reorder the terms: -138 + 9w + 2w2 = 0 Solving -138 + 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'. -69 + 4.5w + w2 = 0 Move the constant term to the right: Add '69' to each side of the equation. -69 + 4.5w + 69 + w2 = 0 + 69 Reorder the terms: -69 + 69 + 4.5w + w2 = 0 + 69 Combine like terms: -69 + 69 = 0 0 + 4.5w + w2 = 0 + 69 4.5w + w2 = 0 + 69 Combine like terms: 0 + 69 = 69 4.5w + w2 = 69 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 = 69 + 5.0625 Reorder the terms: 5.0625 + 4.5w + w2 = 69 + 5.0625 Combine like terms: 69 + 5.0625 = 74.0625 5.0625 + 4.5w + w2 = 74.0625 Factor a perfect square on the left side: (w + 2.25)(w + 2.25) = 74.0625 Calculate the square root of the right side: 8.605957239 Break this problem into two subproblems by setting (w + 2.25) equal to 8.605957239 and -8.605957239.Subproblem 1
w + 2.25 = 8.605957239 Simplifying w + 2.25 = 8.605957239 Reorder the terms: 2.25 + w = 8.605957239 Solving 2.25 + w = 8.605957239 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 = 8.605957239 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + w = 8.605957239 + -2.25 w = 8.605957239 + -2.25 Combine like terms: 8.605957239 + -2.25 = 6.355957239 w = 6.355957239 Simplifying w = 6.355957239Subproblem 2
w + 2.25 = -8.605957239 Simplifying w + 2.25 = -8.605957239 Reorder the terms: 2.25 + w = -8.605957239 Solving 2.25 + w = -8.605957239 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 = -8.605957239 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + w = -8.605957239 + -2.25 w = -8.605957239 + -2.25 Combine like terms: -8.605957239 + -2.25 = -10.855957239 w = -10.855957239 Simplifying w = -10.855957239Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.355957239, -10.855957239}
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