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Simplifying v2 = 12v + -24 Reorder the terms: v2 = -24 + 12v Solving v2 = -24 + 12v Solving for variable 'v'. Reorder the terms: 24 + -12v + v2 = -24 + 12v + 24 + -12v Reorder the terms: 24 + -12v + v2 = -24 + 24 + 12v + -12v Combine like terms: -24 + 24 = 0 24 + -12v + v2 = 0 + 12v + -12v 24 + -12v + v2 = 12v + -12v Combine like terms: 12v + -12v = 0 24 + -12v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -12v + -24 + v2 = 0 + -24 Reorder the terms: 24 + -24 + -12v + v2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -12v + v2 = 0 + -24 -12v + v2 = 0 + -24 Combine like terms: 0 + -24 = -24 -12v + v2 = -24 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 = -24 + 36 Reorder the terms: 36 + -12v + v2 = -24 + 36 Combine like terms: -24 + 36 = 12 36 + -12v + v2 = 12 Factor a perfect square on the left side: (v + -6)(v + -6) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (v + -6) equal to 3.464101615 and -3.464101615.Subproblem 1
v + -6 = 3.464101615 Simplifying v + -6 = 3.464101615 Reorder the terms: -6 + v = 3.464101615 Solving -6 + v = 3.464101615 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 = 3.464101615 + 6 Combine like terms: -6 + 6 = 0 0 + v = 3.464101615 + 6 v = 3.464101615 + 6 Combine like terms: 3.464101615 + 6 = 9.464101615 v = 9.464101615 Simplifying v = 9.464101615Subproblem 2
v + -6 = -3.464101615 Simplifying v + -6 = -3.464101615 Reorder the terms: -6 + v = -3.464101615 Solving -6 + v = -3.464101615 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 = -3.464101615 + 6 Combine like terms: -6 + 6 = 0 0 + v = -3.464101615 + 6 v = -3.464101615 + 6 Combine like terms: -3.464101615 + 6 = 2.535898385 v = 2.535898385 Simplifying v = 2.535898385Solution
The solution to the problem is based on the solutions from the subproblems. v = {9.464101615, 2.535898385}
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