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Simplifying w2 + 2w + -56 = 0 Reorder the terms: -56 + 2w + w2 = 0 Solving -56 + 2w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 2w + 56 + w2 = 0 + 56 Reorder the terms: -56 + 56 + 2w + w2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 2w + w2 = 0 + 56 2w + w2 = 0 + 56 Combine like terms: 0 + 56 = 56 2w + w2 = 56 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 = 56 + 1 Reorder the terms: 1 + 2w + w2 = 56 + 1 Combine like terms: 56 + 1 = 57 1 + 2w + w2 = 57 Factor a perfect square on the left side: (w + 1)(w + 1) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (w + 1) equal to 7.549834435 and -7.549834435.Subproblem 1
w + 1 = 7.549834435 Simplifying w + 1 = 7.549834435 Reorder the terms: 1 + w = 7.549834435 Solving 1 + w = 7.549834435 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 = 7.549834435 + -1 Combine like terms: 1 + -1 = 0 0 + w = 7.549834435 + -1 w = 7.549834435 + -1 Combine like terms: 7.549834435 + -1 = 6.549834435 w = 6.549834435 Simplifying w = 6.549834435Subproblem 2
w + 1 = -7.549834435 Simplifying w + 1 = -7.549834435 Reorder the terms: 1 + w = -7.549834435 Solving 1 + w = -7.549834435 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 = -7.549834435 + -1 Combine like terms: 1 + -1 = 0 0 + w = -7.549834435 + -1 w = -7.549834435 + -1 Combine like terms: -7.549834435 + -1 = -8.549834435 w = -8.549834435 Simplifying w = -8.549834435Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.549834435, -8.549834435}
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