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Simplifying w2 + 18w + 22 = 0 Reorder the terms: 22 + 18w + w2 = 0 Solving 22 + 18w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + 18w + -22 + w2 = 0 + -22 Reorder the terms: 22 + -22 + 18w + w2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 18w + w2 = 0 + -22 18w + w2 = 0 + -22 Combine like terms: 0 + -22 = -22 18w + w2 = -22 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 = -22 + 81 Reorder the terms: 81 + 18w + w2 = -22 + 81 Combine like terms: -22 + 81 = 59 81 + 18w + w2 = 59 Factor a perfect square on the left side: (w + 9)(w + 9) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (w + 9) equal to 7.681145748 and -7.681145748.Subproblem 1
w + 9 = 7.681145748 Simplifying w + 9 = 7.681145748 Reorder the terms: 9 + w = 7.681145748 Solving 9 + w = 7.681145748 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 = 7.681145748 + -9 Combine like terms: 9 + -9 = 0 0 + w = 7.681145748 + -9 w = 7.681145748 + -9 Combine like terms: 7.681145748 + -9 = -1.318854252 w = -1.318854252 Simplifying w = -1.318854252Subproblem 2
w + 9 = -7.681145748 Simplifying w + 9 = -7.681145748 Reorder the terms: 9 + w = -7.681145748 Solving 9 + w = -7.681145748 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 = -7.681145748 + -9 Combine like terms: 9 + -9 = 0 0 + w = -7.681145748 + -9 w = -7.681145748 + -9 Combine like terms: -7.681145748 + -9 = -16.681145748 w = -16.681145748 Simplifying w = -16.681145748Solution
The solution to the problem is based on the solutions from the subproblems. w = {-1.318854252, -16.681145748}
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