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Simplifying w2 + 2w + -324 = 0 Reorder the terms: -324 + 2w + w2 = 0 Solving -324 + 2w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '324' to each side of the equation. -324 + 2w + 324 + w2 = 0 + 324 Reorder the terms: -324 + 324 + 2w + w2 = 0 + 324 Combine like terms: -324 + 324 = 0 0 + 2w + w2 = 0 + 324 2w + w2 = 0 + 324 Combine like terms: 0 + 324 = 324 2w + w2 = 324 The w term is 2w. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2w + 1 + w2 = 324 + 1 Reorder the terms: 1 + 2w + w2 = 324 + 1 Combine like terms: 324 + 1 = 325 1 + 2w + w2 = 325 Factor a perfect square on the left side: (w + 1)(w + 1) = 325 Calculate the square root of the right side: 18.027756377 Break this problem into two subproblems by setting (w + 1) equal to 18.027756377 and -18.027756377.Subproblem 1
w + 1 = 18.027756377 Simplifying w + 1 = 18.027756377 Reorder the terms: 1 + w = 18.027756377 Solving 1 + w = 18.027756377 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 18.027756377 + -1 Combine like terms: 1 + -1 = 0 0 + w = 18.027756377 + -1 w = 18.027756377 + -1 Combine like terms: 18.027756377 + -1 = 17.027756377 w = 17.027756377 Simplifying w = 17.027756377Subproblem 2
w + 1 = -18.027756377 Simplifying w + 1 = -18.027756377 Reorder the terms: 1 + w = -18.027756377 Solving 1 + w = -18.027756377 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = -18.027756377 + -1 Combine like terms: 1 + -1 = 0 0 + w = -18.027756377 + -1 w = -18.027756377 + -1 Combine like terms: -18.027756377 + -1 = -19.027756377 w = -19.027756377 Simplifying w = -19.027756377Solution
The solution to the problem is based on the solutions from the subproblems. w = {17.027756377, -19.027756377}
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