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Simplifying 2v2 + -12v + 2 = (v + -3) Reorder the terms: 2 + -12v + 2v2 = (v + -3) Reorder the terms: 2 + -12v + 2v2 = (-3 + v) Remove parenthesis around (-3 + v) 2 + -12v + 2v2 = -3 + v Solving 2 + -12v + 2v2 = -3 + v Solving for variable 'v'. Reorder the terms: 2 + 3 + -12v + -1v + 2v2 = -3 + v + 3 + -1v Combine like terms: 2 + 3 = 5 5 + -12v + -1v + 2v2 = -3 + v + 3 + -1v Combine like terms: -12v + -1v = -13v 5 + -13v + 2v2 = -3 + v + 3 + -1v Reorder the terms: 5 + -13v + 2v2 = -3 + 3 + v + -1v Combine like terms: -3 + 3 = 0 5 + -13v + 2v2 = 0 + v + -1v 5 + -13v + 2v2 = v + -1v Combine like terms: v + -1v = 0 5 + -13v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -6.5v + v2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -6.5v + -2.5 + v2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -6.5v + v2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -6.5v + v2 = 0 + -2.5 -6.5v + v2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -6.5v + v2 = -2.5 The v term is -6.5v. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5v + 10.5625 + v2 = -2.5 + 10.5625 Reorder the terms: 10.5625 + -6.5v + v2 = -2.5 + 10.5625 Combine like terms: -2.5 + 10.5625 = 8.0625 10.5625 + -6.5v + v2 = 8.0625 Factor a perfect square on the left side: (v + -3.25)(v + -3.25) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (v + -3.25) equal to 2.839454173 and -2.839454173.Subproblem 1
v + -3.25 = 2.839454173 Simplifying v + -3.25 = 2.839454173 Reorder the terms: -3.25 + v = 2.839454173 Solving -3.25 + v = 2.839454173 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + v = 2.839454173 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + v = 2.839454173 + 3.25 v = 2.839454173 + 3.25 Combine like terms: 2.839454173 + 3.25 = 6.089454173 v = 6.089454173 Simplifying v = 6.089454173Subproblem 2
v + -3.25 = -2.839454173 Simplifying v + -3.25 = -2.839454173 Reorder the terms: -3.25 + v = -2.839454173 Solving -3.25 + v = -2.839454173 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + v = -2.839454173 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + v = -2.839454173 + 3.25 v = -2.839454173 + 3.25 Combine like terms: -2.839454173 + 3.25 = 0.410545827 v = 0.410545827 Simplifying v = 0.410545827Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.089454173, 0.410545827}
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