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Simplifying v2 + -19v = 23 Reorder the terms: -19v + v2 = 23 Solving -19v + v2 = 23 Solving for variable 'v'. Reorder the terms: -23 + -19v + v2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + -19v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -19v + 23 + v2 = 0 + 23 Reorder the terms: -23 + 23 + -19v + v2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -19v + v2 = 0 + 23 -19v + v2 = 0 + 23 Combine like terms: 0 + 23 = 23 -19v + v2 = 23 The v term is -19v. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19v + 90.25 + v2 = 23 + 90.25 Reorder the terms: 90.25 + -19v + v2 = 23 + 90.25 Combine like terms: 23 + 90.25 = 113.25 90.25 + -19v + v2 = 113.25 Factor a perfect square on the left side: (v + -9.5)(v + -9.5) = 113.25 Calculate the square root of the right side: 10.641898327 Break this problem into two subproblems by setting (v + -9.5) equal to 10.641898327 and -10.641898327.Subproblem 1
v + -9.5 = 10.641898327 Simplifying v + -9.5 = 10.641898327 Reorder the terms: -9.5 + v = 10.641898327 Solving -9.5 + v = 10.641898327 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + v = 10.641898327 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + v = 10.641898327 + 9.5 v = 10.641898327 + 9.5 Combine like terms: 10.641898327 + 9.5 = 20.141898327 v = 20.141898327 Simplifying v = 20.141898327Subproblem 2
v + -9.5 = -10.641898327 Simplifying v + -9.5 = -10.641898327 Reorder the terms: -9.5 + v = -10.641898327 Solving -9.5 + v = -10.641898327 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + v = -10.641898327 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + v = -10.641898327 + 9.5 v = -10.641898327 + 9.5 Combine like terms: -10.641898327 + 9.5 = -1.141898327 v = -1.141898327 Simplifying v = -1.141898327Solution
The solution to the problem is based on the solutions from the subproblems. v = {20.141898327, -1.141898327}
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