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Simplifying v2 + -22v + -43 = 0 Reorder the terms: -43 + -22v + v2 = 0 Solving -43 + -22v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -22v + 43 + v2 = 0 + 43 Reorder the terms: -43 + 43 + -22v + v2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -22v + v2 = 0 + 43 -22v + v2 = 0 + 43 Combine like terms: 0 + 43 = 43 -22v + v2 = 43 The v term is -22v. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22v + 121 + v2 = 43 + 121 Reorder the terms: 121 + -22v + v2 = 43 + 121 Combine like terms: 43 + 121 = 164 121 + -22v + v2 = 164 Factor a perfect square on the left side: (v + -11)(v + -11) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (v + -11) equal to 12.806248475 and -12.806248475.Subproblem 1
v + -11 = 12.806248475 Simplifying v + -11 = 12.806248475 Reorder the terms: -11 + v = 12.806248475 Solving -11 + v = 12.806248475 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + v = 12.806248475 + 11 Combine like terms: -11 + 11 = 0 0 + v = 12.806248475 + 11 v = 12.806248475 + 11 Combine like terms: 12.806248475 + 11 = 23.806248475 v = 23.806248475 Simplifying v = 23.806248475Subproblem 2
v + -11 = -12.806248475 Simplifying v + -11 = -12.806248475 Reorder the terms: -11 + v = -12.806248475 Solving -11 + v = -12.806248475 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + v = -12.806248475 + 11 Combine like terms: -11 + 11 = 0 0 + v = -12.806248475 + 11 v = -12.806248475 + 11 Combine like terms: -12.806248475 + 11 = -1.806248475 v = -1.806248475 Simplifying v = -1.806248475Solution
The solution to the problem is based on the solutions from the subproblems. v = {23.806248475, -1.806248475}
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