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Simplifying w2 + -4w + -172 = 0 Reorder the terms: -172 + -4w + w2 = 0 Solving -172 + -4w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '172' to each side of the equation. -172 + -4w + 172 + w2 = 0 + 172 Reorder the terms: -172 + 172 + -4w + w2 = 0 + 172 Combine like terms: -172 + 172 = 0 0 + -4w + w2 = 0 + 172 -4w + w2 = 0 + 172 Combine like terms: 0 + 172 = 172 -4w + w2 = 172 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 = 172 + 4 Reorder the terms: 4 + -4w + w2 = 172 + 4 Combine like terms: 172 + 4 = 176 4 + -4w + w2 = 176 Factor a perfect square on the left side: (w + -2)(w + -2) = 176 Calculate the square root of the right side: 13.266499161 Break this problem into two subproblems by setting (w + -2) equal to 13.266499161 and -13.266499161.Subproblem 1
w + -2 = 13.266499161 Simplifying w + -2 = 13.266499161 Reorder the terms: -2 + w = 13.266499161 Solving -2 + w = 13.266499161 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 = 13.266499161 + 2 Combine like terms: -2 + 2 = 0 0 + w = 13.266499161 + 2 w = 13.266499161 + 2 Combine like terms: 13.266499161 + 2 = 15.266499161 w = 15.266499161 Simplifying w = 15.266499161Subproblem 2
w + -2 = -13.266499161 Simplifying w + -2 = -13.266499161 Reorder the terms: -2 + w = -13.266499161 Solving -2 + w = -13.266499161 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 = -13.266499161 + 2 Combine like terms: -2 + 2 = 0 0 + w = -13.266499161 + 2 w = -13.266499161 + 2 Combine like terms: -13.266499161 + 2 = -11.266499161 w = -11.266499161 Simplifying w = -11.266499161Solution
The solution to the problem is based on the solutions from the subproblems. w = {15.266499161, -11.266499161}
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