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Simplifying (w * w) + -4w + -11 = 0 Multiply w * w (w2) + -4w + -11 = 0 w2 + -4w + -11 = 0 Reorder the terms: -11 + -4w + w2 = 0 Solving -11 + -4w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -4w + 11 + w2 = 0 + 11 Reorder the terms: -11 + 11 + -4w + w2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -4w + w2 = 0 + 11 -4w + w2 = 0 + 11 Combine like terms: 0 + 11 = 11 -4w + w2 = 11 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 = 11 + 4 Reorder the terms: 4 + -4w + w2 = 11 + 4 Combine like terms: 11 + 4 = 15 4 + -4w + w2 = 15 Factor a perfect square on the left side: (w + -2)(w + -2) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (w + -2) equal to 3.872983346 and -3.872983346.Subproblem 1
w + -2 = 3.872983346 Simplifying w + -2 = 3.872983346 Reorder the terms: -2 + w = 3.872983346 Solving -2 + w = 3.872983346 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 = 3.872983346 + 2 Combine like terms: -2 + 2 = 0 0 + w = 3.872983346 + 2 w = 3.872983346 + 2 Combine like terms: 3.872983346 + 2 = 5.872983346 w = 5.872983346 Simplifying w = 5.872983346Subproblem 2
w + -2 = -3.872983346 Simplifying w + -2 = -3.872983346 Reorder the terms: -2 + w = -3.872983346 Solving -2 + w = -3.872983346 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 = -3.872983346 + 2 Combine like terms: -2 + 2 = 0 0 + w = -3.872983346 + 2 w = -3.872983346 + 2 Combine like terms: -3.872983346 + 2 = -1.872983346 w = -1.872983346 Simplifying w = -1.872983346Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.872983346, -1.872983346}
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