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Simplifying v2 + -18v + 32 = -2 Reorder the terms: 32 + -18v + v2 = -2 Solving 32 + -18v + v2 = -2 Solving for variable 'v'. Reorder the terms: 32 + 2 + -18v + v2 = -2 + 2 Combine like terms: 32 + 2 = 34 34 + -18v + v2 = -2 + 2 Combine like terms: -2 + 2 = 0 34 + -18v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + -18v + -34 + v2 = 0 + -34 Reorder the terms: 34 + -34 + -18v + v2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -18v + v2 = 0 + -34 -18v + v2 = 0 + -34 Combine like terms: 0 + -34 = -34 -18v + v2 = -34 The v term is -18v. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18v + 81 + v2 = -34 + 81 Reorder the terms: 81 + -18v + v2 = -34 + 81 Combine like terms: -34 + 81 = 47 81 + -18v + v2 = 47 Factor a perfect square on the left side: (v + -9)(v + -9) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (v + -9) equal to 6.8556546 and -6.8556546.Subproblem 1
v + -9 = 6.8556546 Simplifying v + -9 = 6.8556546 Reorder the terms: -9 + v = 6.8556546 Solving -9 + v = 6.8556546 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + v = 6.8556546 + 9 Combine like terms: -9 + 9 = 0 0 + v = 6.8556546 + 9 v = 6.8556546 + 9 Combine like terms: 6.8556546 + 9 = 15.8556546 v = 15.8556546 Simplifying v = 15.8556546Subproblem 2
v + -9 = -6.8556546 Simplifying v + -9 = -6.8556546 Reorder the terms: -9 + v = -6.8556546 Solving -9 + v = -6.8556546 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + v = -6.8556546 + 9 Combine like terms: -9 + 9 = 0 0 + v = -6.8556546 + 9 v = -6.8556546 + 9 Combine like terms: -6.8556546 + 9 = 2.1443454 v = 2.1443454 Simplifying v = 2.1443454Solution
The solution to the problem is based on the solutions from the subproblems. v = {15.8556546, 2.1443454}
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