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Simplifying w2 + -2w + -112 = 0 Reorder the terms: -112 + -2w + w2 = 0 Solving -112 + -2w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '112' to each side of the equation. -112 + -2w + 112 + w2 = 0 + 112 Reorder the terms: -112 + 112 + -2w + w2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + -2w + w2 = 0 + 112 -2w + w2 = 0 + 112 Combine like terms: 0 + 112 = 112 -2w + w2 = 112 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 = 112 + 1 Reorder the terms: 1 + -2w + w2 = 112 + 1 Combine like terms: 112 + 1 = 113 1 + -2w + w2 = 113 Factor a perfect square on the left side: (w + -1)(w + -1) = 113 Calculate the square root of the right side: 10.630145813 Break this problem into two subproblems by setting (w + -1) equal to 10.630145813 and -10.630145813.Subproblem 1
w + -1 = 10.630145813 Simplifying w + -1 = 10.630145813 Reorder the terms: -1 + w = 10.630145813 Solving -1 + w = 10.630145813 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 = 10.630145813 + 1 Combine like terms: -1 + 1 = 0 0 + w = 10.630145813 + 1 w = 10.630145813 + 1 Combine like terms: 10.630145813 + 1 = 11.630145813 w = 11.630145813 Simplifying w = 11.630145813Subproblem 2
w + -1 = -10.630145813 Simplifying w + -1 = -10.630145813 Reorder the terms: -1 + w = -10.630145813 Solving -1 + w = -10.630145813 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 = -10.630145813 + 1 Combine like terms: -1 + 1 = 0 0 + w = -10.630145813 + 1 w = -10.630145813 + 1 Combine like terms: -10.630145813 + 1 = -9.630145813 w = -9.630145813 Simplifying w = -9.630145813Solution
The solution to the problem is based on the solutions from the subproblems. w = {11.630145813, -9.630145813}
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