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Simplifying 3v2 + -6v + -2 = 0 Reorder the terms: -2 + -6v + 3v2 = 0 Solving -2 + -6v + 3v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + -2v + v2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -2v + 0.6666666667 + v2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -2v + v2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -2v + v2 = 0 + 0.6666666667 -2v + v2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -2v + v2 = 0.6666666667 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 = 0.6666666667 + 1 Reorder the terms: 1 + -2v + v2 = 0.6666666667 + 1 Combine like terms: 0.6666666667 + 1 = 1.6666666667 1 + -2v + v2 = 1.6666666667 Factor a perfect square on the left side: (v + -1)(v + -1) = 1.6666666667 Calculate the square root of the right side: 1.290994449 Break this problem into two subproblems by setting (v + -1) equal to 1.290994449 and -1.290994449.Subproblem 1
v + -1 = 1.290994449 Simplifying v + -1 = 1.290994449 Reorder the terms: -1 + v = 1.290994449 Solving -1 + v = 1.290994449 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 = 1.290994449 + 1 Combine like terms: -1 + 1 = 0 0 + v = 1.290994449 + 1 v = 1.290994449 + 1 Combine like terms: 1.290994449 + 1 = 2.290994449 v = 2.290994449 Simplifying v = 2.290994449Subproblem 2
v + -1 = -1.290994449 Simplifying v + -1 = -1.290994449 Reorder the terms: -1 + v = -1.290994449 Solving -1 + v = -1.290994449 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 = -1.290994449 + 1 Combine like terms: -1 + 1 = 0 0 + v = -1.290994449 + 1 v = -1.290994449 + 1 Combine like terms: -1.290994449 + 1 = -0.290994449 v = -0.290994449 Simplifying v = -0.290994449Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.290994449, -0.290994449}
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