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Simplifying w2 + w + -112 = 0 Reorder the terms: -112 + w + w2 = 0 Solving -112 + w + 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 + w + 112 + w2 = 0 + 112 Reorder the terms: -112 + 112 + w + w2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + w + w2 = 0 + 112 w + w2 = 0 + 112 Combine like terms: 0 + 112 = 112 w + w2 = 112 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. w + 0.25 + w2 = 112 + 0.25 Reorder the terms: 0.25 + w + w2 = 112 + 0.25 Combine like terms: 112 + 0.25 = 112.25 0.25 + w + w2 = 112.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 112.25 Calculate the square root of the right side: 10.59481005 Break this problem into two subproblems by setting (w + 0.5) equal to 10.59481005 and -10.59481005.Subproblem 1
w + 0.5 = 10.59481005 Simplifying w + 0.5 = 10.59481005 Reorder the terms: 0.5 + w = 10.59481005 Solving 0.5 + w = 10.59481005 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 10.59481005 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 10.59481005 + -0.5 w = 10.59481005 + -0.5 Combine like terms: 10.59481005 + -0.5 = 10.09481005 w = 10.09481005 Simplifying w = 10.09481005Subproblem 2
w + 0.5 = -10.59481005 Simplifying w + 0.5 = -10.59481005 Reorder the terms: 0.5 + w = -10.59481005 Solving 0.5 + w = -10.59481005 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -10.59481005 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -10.59481005 + -0.5 w = -10.59481005 + -0.5 Combine like terms: -10.59481005 + -0.5 = -11.09481005 w = -11.09481005 Simplifying w = -11.09481005Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.09481005, -11.09481005}
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