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Simplifying v2 + 12v + -30 = 0 Reorder the terms: -30 + 12v + v2 = 0 Solving -30 + 12v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 12v + 30 + v2 = 0 + 30 Reorder the terms: -30 + 30 + 12v + v2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 12v + v2 = 0 + 30 12v + v2 = 0 + 30 Combine like terms: 0 + 30 = 30 12v + v2 = 30 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 = 30 + 36 Reorder the terms: 36 + 12v + v2 = 30 + 36 Combine like terms: 30 + 36 = 66 36 + 12v + v2 = 66 Factor a perfect square on the left side: (v + 6)(v + 6) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (v + 6) equal to 8.124038405 and -8.124038405.Subproblem 1
v + 6 = 8.124038405 Simplifying v + 6 = 8.124038405 Reorder the terms: 6 + v = 8.124038405 Solving 6 + v = 8.124038405 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 = 8.124038405 + -6 Combine like terms: 6 + -6 = 0 0 + v = 8.124038405 + -6 v = 8.124038405 + -6 Combine like terms: 8.124038405 + -6 = 2.124038405 v = 2.124038405 Simplifying v = 2.124038405Subproblem 2
v + 6 = -8.124038405 Simplifying v + 6 = -8.124038405 Reorder the terms: 6 + v = -8.124038405 Solving 6 + v = -8.124038405 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 = -8.124038405 + -6 Combine like terms: 6 + -6 = 0 0 + v = -8.124038405 + -6 v = -8.124038405 + -6 Combine like terms: -8.124038405 + -6 = -14.124038405 v = -14.124038405 Simplifying v = -14.124038405Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.124038405, -14.124038405}
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