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Simplifying v2 + 12v + 12 = 0 Reorder the terms: 12 + 12v + v2 = 0 Solving 12 + 12v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 12v + -12 + v2 = 0 + -12 Reorder the terms: 12 + -12 + 12v + v2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 12v + v2 = 0 + -12 12v + v2 = 0 + -12 Combine like terms: 0 + -12 = -12 12v + v2 = -12 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 = -12 + 36 Reorder the terms: 36 + 12v + v2 = -12 + 36 Combine like terms: -12 + 36 = 24 36 + 12v + v2 = 24 Factor a perfect square on the left side: (v + 6)(v + 6) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (v + 6) equal to 4.898979486 and -4.898979486.Subproblem 1
v + 6 = 4.898979486 Simplifying v + 6 = 4.898979486 Reorder the terms: 6 + v = 4.898979486 Solving 6 + v = 4.898979486 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 = 4.898979486 + -6 Combine like terms: 6 + -6 = 0 0 + v = 4.898979486 + -6 v = 4.898979486 + -6 Combine like terms: 4.898979486 + -6 = -1.101020514 v = -1.101020514 Simplifying v = -1.101020514Subproblem 2
v + 6 = -4.898979486 Simplifying v + 6 = -4.898979486 Reorder the terms: 6 + v = -4.898979486 Solving 6 + v = -4.898979486 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 = -4.898979486 + -6 Combine like terms: 6 + -6 = 0 0 + v = -4.898979486 + -6 v = -4.898979486 + -6 Combine like terms: -4.898979486 + -6 = -10.898979486 v = -10.898979486 Simplifying v = -10.898979486Solution
The solution to the problem is based on the solutions from the subproblems. v = {-1.101020514, -10.898979486}
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