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Simplifying w2 + 3w + -324 = 0 Reorder the terms: -324 + 3w + w2 = 0 Solving -324 + 3w + 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 + 3w + 324 + w2 = 0 + 324 Reorder the terms: -324 + 324 + 3w + w2 = 0 + 324 Combine like terms: -324 + 324 = 0 0 + 3w + w2 = 0 + 324 3w + w2 = 0 + 324 Combine like terms: 0 + 324 = 324 3w + w2 = 324 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = 324 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 324 + 2.25 Combine like terms: 324 + 2.25 = 326.25 2.25 + 3w + w2 = 326.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 326.25 Calculate the square root of the right side: 18.062391868 Break this problem into two subproblems by setting (w + 1.5) equal to 18.062391868 and -18.062391868.Subproblem 1
w + 1.5 = 18.062391868 Simplifying w + 1.5 = 18.062391868 Reorder the terms: 1.5 + w = 18.062391868 Solving 1.5 + w = 18.062391868 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 18.062391868 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 18.062391868 + -1.5 w = 18.062391868 + -1.5 Combine like terms: 18.062391868 + -1.5 = 16.562391868 w = 16.562391868 Simplifying w = 16.562391868Subproblem 2
w + 1.5 = -18.062391868 Simplifying w + 1.5 = -18.062391868 Reorder the terms: 1.5 + w = -18.062391868 Solving 1.5 + w = -18.062391868 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -18.062391868 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -18.062391868 + -1.5 w = -18.062391868 + -1.5 Combine like terms: -18.062391868 + -1.5 = -19.562391868 w = -19.562391868 Simplifying w = -19.562391868Solution
The solution to the problem is based on the solutions from the subproblems. w = {16.562391868, -19.562391868}
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