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Simplifying w2 + -4w = 112 Reorder the terms: -4w + w2 = 112 Solving -4w + w2 = 112 Solving for variable 'w'. Reorder the terms: -112 + -4w + w2 = 112 + -112 Combine like terms: 112 + -112 = 0 -112 + -4w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '112' to each side of the equation. -112 + -4w + 112 + w2 = 0 + 112 Reorder the terms: -112 + 112 + -4w + w2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + -4w + w2 = 0 + 112 -4w + w2 = 0 + 112 Combine like terms: 0 + 112 = 112 -4w + w2 = 112 The w term is -4w. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4w + 4 + w2 = 112 + 4 Reorder the terms: 4 + -4w + w2 = 112 + 4 Combine like terms: 112 + 4 = 116 4 + -4w + w2 = 116 Factor a perfect square on the left side: (w + -2)(w + -2) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (w + -2) equal to 10.770329614 and -10.770329614.Subproblem 1
w + -2 = 10.770329614 Simplifying w + -2 = 10.770329614 Reorder the terms: -2 + w = 10.770329614 Solving -2 + w = 10.770329614 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 10.770329614 + 2 Combine like terms: -2 + 2 = 0 0 + w = 10.770329614 + 2 w = 10.770329614 + 2 Combine like terms: 10.770329614 + 2 = 12.770329614 w = 12.770329614 Simplifying w = 12.770329614Subproblem 2
w + -2 = -10.770329614 Simplifying w + -2 = -10.770329614 Reorder the terms: -2 + w = -10.770329614 Solving -2 + w = -10.770329614 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = -10.770329614 + 2 Combine like terms: -2 + 2 = 0 0 + w = -10.770329614 + 2 w = -10.770329614 + 2 Combine like terms: -10.770329614 + 2 = -8.770329614 w = -8.770329614 Simplifying w = -8.770329614Solution
The solution to the problem is based on the solutions from the subproblems. w = {12.770329614, -8.770329614}
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