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Simplifying w2 + 18w + -5 = 0 Reorder the terms: -5 + 18w + w2 = 0 Solving -5 + 18w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 18w + 5 + w2 = 0 + 5 Reorder the terms: -5 + 5 + 18w + w2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 18w + w2 = 0 + 5 18w + w2 = 0 + 5 Combine like terms: 0 + 5 = 5 18w + w2 = 5 The w term is 18w. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18w + 81 + w2 = 5 + 81 Reorder the terms: 81 + 18w + w2 = 5 + 81 Combine like terms: 5 + 81 = 86 81 + 18w + w2 = 86 Factor a perfect square on the left side: (w + 9)(w + 9) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (w + 9) equal to 9.273618495 and -9.273618495.Subproblem 1
w + 9 = 9.273618495 Simplifying w + 9 = 9.273618495 Reorder the terms: 9 + w = 9.273618495 Solving 9 + w = 9.273618495 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + w = 9.273618495 + -9 Combine like terms: 9 + -9 = 0 0 + w = 9.273618495 + -9 w = 9.273618495 + -9 Combine like terms: 9.273618495 + -9 = 0.273618495 w = 0.273618495 Simplifying w = 0.273618495Subproblem 2
w + 9 = -9.273618495 Simplifying w + 9 = -9.273618495 Reorder the terms: 9 + w = -9.273618495 Solving 9 + w = -9.273618495 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + w = -9.273618495 + -9 Combine like terms: 9 + -9 = 0 0 + w = -9.273618495 + -9 w = -9.273618495 + -9 Combine like terms: -9.273618495 + -9 = -18.273618495 w = -18.273618495 Simplifying w = -18.273618495Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.273618495, -18.273618495}
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