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Simplifying v2 + -12v = 3 Reorder the terms: -12v + v2 = 3 Solving -12v + v2 = 3 Solving for variable 'v'. Reorder the terms: -3 + -12v + v2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -12v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -12v + 3 + v2 = 0 + 3 Reorder the terms: -3 + 3 + -12v + v2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -12v + v2 = 0 + 3 -12v + v2 = 0 + 3 Combine like terms: 0 + 3 = 3 -12v + v2 = 3 The v term is -12v. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12v + 36 + v2 = 3 + 36 Reorder the terms: 36 + -12v + v2 = 3 + 36 Combine like terms: 3 + 36 = 39 36 + -12v + v2 = 39 Factor a perfect square on the left side: (v + -6)(v + -6) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (v + -6) equal to 6.244997998 and -6.244997998.Subproblem 1
v + -6 = 6.244997998 Simplifying v + -6 = 6.244997998 Reorder the terms: -6 + v = 6.244997998 Solving -6 + v = 6.244997998 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + v = 6.244997998 + 6 Combine like terms: -6 + 6 = 0 0 + v = 6.244997998 + 6 v = 6.244997998 + 6 Combine like terms: 6.244997998 + 6 = 12.244997998 v = 12.244997998 Simplifying v = 12.244997998Subproblem 2
v + -6 = -6.244997998 Simplifying v + -6 = -6.244997998 Reorder the terms: -6 + v = -6.244997998 Solving -6 + v = -6.244997998 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + v = -6.244997998 + 6 Combine like terms: -6 + 6 = 0 0 + v = -6.244997998 + 6 v = -6.244997998 + 6 Combine like terms: -6.244997998 + 6 = -0.244997998 v = -0.244997998 Simplifying v = -0.244997998Solution
The solution to the problem is based on the solutions from the subproblems. v = {12.244997998, -0.244997998}
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