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Simplifying -164 + w2 + 18w = 0 Reorder the terms: -164 + 18w + w2 = 0 Solving -164 + 18w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '164' to each side of the equation. -164 + 18w + 164 + w2 = 0 + 164 Reorder the terms: -164 + 164 + 18w + w2 = 0 + 164 Combine like terms: -164 + 164 = 0 0 + 18w + w2 = 0 + 164 18w + w2 = 0 + 164 Combine like terms: 0 + 164 = 164 18w + w2 = 164 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 = 164 + 81 Reorder the terms: 81 + 18w + w2 = 164 + 81 Combine like terms: 164 + 81 = 245 81 + 18w + w2 = 245 Factor a perfect square on the left side: (w + 9)(w + 9) = 245 Calculate the square root of the right side: 15.652475842 Break this problem into two subproblems by setting (w + 9) equal to 15.652475842 and -15.652475842.Subproblem 1
w + 9 = 15.652475842 Simplifying w + 9 = 15.652475842 Reorder the terms: 9 + w = 15.652475842 Solving 9 + w = 15.652475842 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 = 15.652475842 + -9 Combine like terms: 9 + -9 = 0 0 + w = 15.652475842 + -9 w = 15.652475842 + -9 Combine like terms: 15.652475842 + -9 = 6.652475842 w = 6.652475842 Simplifying w = 6.652475842Subproblem 2
w + 9 = -15.652475842 Simplifying w + 9 = -15.652475842 Reorder the terms: 9 + w = -15.652475842 Solving 9 + w = -15.652475842 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 = -15.652475842 + -9 Combine like terms: 9 + -9 = 0 0 + w = -15.652475842 + -9 w = -15.652475842 + -9 Combine like terms: -15.652475842 + -9 = -24.652475842 w = -24.652475842 Simplifying w = -24.652475842Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.652475842, -24.652475842}
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