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Simplifying v2 + 10v + 2 = 0 Reorder the terms: 2 + 10v + v2 = 0 Solving 2 + 10v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 10v + -2 + v2 = 0 + -2 Reorder the terms: 2 + -2 + 10v + v2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 10v + v2 = 0 + -2 10v + v2 = 0 + -2 Combine like terms: 0 + -2 = -2 10v + v2 = -2 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 = -2 + 25 Reorder the terms: 25 + 10v + v2 = -2 + 25 Combine like terms: -2 + 25 = 23 25 + 10v + v2 = 23 Factor a perfect square on the left side: (v + 5)(v + 5) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (v + 5) equal to 4.795831523 and -4.795831523.Subproblem 1
v + 5 = 4.795831523 Simplifying v + 5 = 4.795831523 Reorder the terms: 5 + v = 4.795831523 Solving 5 + v = 4.795831523 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 = 4.795831523 + -5 Combine like terms: 5 + -5 = 0 0 + v = 4.795831523 + -5 v = 4.795831523 + -5 Combine like terms: 4.795831523 + -5 = -0.204168477 v = -0.204168477 Simplifying v = -0.204168477Subproblem 2
v + 5 = -4.795831523 Simplifying v + 5 = -4.795831523 Reorder the terms: 5 + v = -4.795831523 Solving 5 + v = -4.795831523 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 = -4.795831523 + -5 Combine like terms: 5 + -5 = 0 0 + v = -4.795831523 + -5 v = -4.795831523 + -5 Combine like terms: -4.795831523 + -5 = -9.795831523 v = -9.795831523 Simplifying v = -9.795831523Solution
The solution to the problem is based on the solutions from the subproblems. v = {-0.204168477, -9.795831523}
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