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Simplifying w2 + 2w + -390 = 0 Reorder the terms: -390 + 2w + w2 = 0 Solving -390 + 2w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '390' to each side of the equation. -390 + 2w + 390 + w2 = 0 + 390 Reorder the terms: -390 + 390 + 2w + w2 = 0 + 390 Combine like terms: -390 + 390 = 0 0 + 2w + w2 = 0 + 390 2w + w2 = 0 + 390 Combine like terms: 0 + 390 = 390 2w + w2 = 390 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 = 390 + 1 Reorder the terms: 1 + 2w + w2 = 390 + 1 Combine like terms: 390 + 1 = 391 1 + 2w + w2 = 391 Factor a perfect square on the left side: (w + 1)(w + 1) = 391 Calculate the square root of the right side: 19.773719933 Break this problem into two subproblems by setting (w + 1) equal to 19.773719933 and -19.773719933.Subproblem 1
w + 1 = 19.773719933 Simplifying w + 1 = 19.773719933 Reorder the terms: 1 + w = 19.773719933 Solving 1 + w = 19.773719933 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 = 19.773719933 + -1 Combine like terms: 1 + -1 = 0 0 + w = 19.773719933 + -1 w = 19.773719933 + -1 Combine like terms: 19.773719933 + -1 = 18.773719933 w = 18.773719933 Simplifying w = 18.773719933Subproblem 2
w + 1 = -19.773719933 Simplifying w + 1 = -19.773719933 Reorder the terms: 1 + w = -19.773719933 Solving 1 + w = -19.773719933 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 = -19.773719933 + -1 Combine like terms: 1 + -1 = 0 0 + w = -19.773719933 + -1 w = -19.773719933 + -1 Combine like terms: -19.773719933 + -1 = -20.773719933 w = -20.773719933 Simplifying w = -20.773719933Solution
The solution to the problem is based on the solutions from the subproblems. w = {18.773719933, -20.773719933}
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