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Simplifying 5v2 + -10v + -12 = 0 Reorder the terms: -12 + -10v + 5v2 = 0 Solving -12 + -10v + 5v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + -2v + v2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -2v + 2.4 + v2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -2v + v2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -2v + v2 = 0 + 2.4 -2v + v2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -2v + v2 = 2.4 The v term is -2v. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2v + 1 + v2 = 2.4 + 1 Reorder the terms: 1 + -2v + v2 = 2.4 + 1 Combine like terms: 2.4 + 1 = 3.4 1 + -2v + v2 = 3.4 Factor a perfect square on the left side: (v + -1)(v + -1) = 3.4 Calculate the square root of the right side: 1.843908891 Break this problem into two subproblems by setting (v + -1) equal to 1.843908891 and -1.843908891.Subproblem 1
v + -1 = 1.843908891 Simplifying v + -1 = 1.843908891 Reorder the terms: -1 + v = 1.843908891 Solving -1 + v = 1.843908891 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + v = 1.843908891 + 1 Combine like terms: -1 + 1 = 0 0 + v = 1.843908891 + 1 v = 1.843908891 + 1 Combine like terms: 1.843908891 + 1 = 2.843908891 v = 2.843908891 Simplifying v = 2.843908891Subproblem 2
v + -1 = -1.843908891 Simplifying v + -1 = -1.843908891 Reorder the terms: -1 + v = -1.843908891 Solving -1 + v = -1.843908891 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + v = -1.843908891 + 1 Combine like terms: -1 + 1 = 0 0 + v = -1.843908891 + 1 v = -1.843908891 + 1 Combine like terms: -1.843908891 + 1 = -0.843908891 v = -0.843908891 Simplifying v = -0.843908891Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.843908891, -0.843908891}
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