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Simplifying w2 + 8w + -40 = 0 Reorder the terms: -40 + 8w + w2 = 0 Solving -40 + 8w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 8w + 40 + w2 = 0 + 40 Reorder the terms: -40 + 40 + 8w + w2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 8w + w2 = 0 + 40 8w + w2 = 0 + 40 Combine like terms: 0 + 40 = 40 8w + w2 = 40 The w term is 8w. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8w + 16 + w2 = 40 + 16 Reorder the terms: 16 + 8w + w2 = 40 + 16 Combine like terms: 40 + 16 = 56 16 + 8w + w2 = 56 Factor a perfect square on the left side: (w + 4)(w + 4) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (w + 4) equal to 7.483314774 and -7.483314774.Subproblem 1
w + 4 = 7.483314774 Simplifying w + 4 = 7.483314774 Reorder the terms: 4 + w = 7.483314774 Solving 4 + w = 7.483314774 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = 7.483314774 + -4 Combine like terms: 4 + -4 = 0 0 + w = 7.483314774 + -4 w = 7.483314774 + -4 Combine like terms: 7.483314774 + -4 = 3.483314774 w = 3.483314774 Simplifying w = 3.483314774Subproblem 2
w + 4 = -7.483314774 Simplifying w + 4 = -7.483314774 Reorder the terms: 4 + w = -7.483314774 Solving 4 + w = -7.483314774 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = -7.483314774 + -4 Combine like terms: 4 + -4 = 0 0 + w = -7.483314774 + -4 w = -7.483314774 + -4 Combine like terms: -7.483314774 + -4 = -11.483314774 w = -11.483314774 Simplifying w = -11.483314774Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.483314774, -11.483314774}
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