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Simplifying v2 + -10v + -1 = 0 Reorder the terms: -1 + -10v + v2 = 0 Solving -1 + -10v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -10v + 1 + v2 = 0 + 1 Reorder the terms: -1 + 1 + -10v + v2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -10v + v2 = 0 + 1 -10v + v2 = 0 + 1 Combine like terms: 0 + 1 = 1 -10v + v2 = 1 The v term is -10v. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10v + 25 + v2 = 1 + 25 Reorder the terms: 25 + -10v + v2 = 1 + 25 Combine like terms: 1 + 25 = 26 25 + -10v + v2 = 26 Factor a perfect square on the left side: (v + -5)(v + -5) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (v + -5) equal to 5.099019514 and -5.099019514.Subproblem 1
v + -5 = 5.099019514 Simplifying v + -5 = 5.099019514 Reorder the terms: -5 + v = 5.099019514 Solving -5 + v = 5.099019514 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + v = 5.099019514 + 5 Combine like terms: -5 + 5 = 0 0 + v = 5.099019514 + 5 v = 5.099019514 + 5 Combine like terms: 5.099019514 + 5 = 10.099019514 v = 10.099019514 Simplifying v = 10.099019514Subproblem 2
v + -5 = -5.099019514 Simplifying v + -5 = -5.099019514 Reorder the terms: -5 + v = -5.099019514 Solving -5 + v = -5.099019514 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + v = -5.099019514 + 5 Combine like terms: -5 + 5 = 0 0 + v = -5.099019514 + 5 v = -5.099019514 + 5 Combine like terms: -5.099019514 + 5 = -0.099019514 v = -0.099019514 Simplifying v = -0.099019514Solution
The solution to the problem is based on the solutions from the subproblems. v = {10.099019514, -0.099019514}
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