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Simplifying 2v2 + 4v + -2 = 5 Reorder the terms: -2 + 4v + 2v2 = 5 Solving -2 + 4v + 2v2 = 5 Solving for variable 'v'. Reorder the terms: -2 + -5 + 4v + 2v2 = 5 + -5 Combine like terms: -2 + -5 = -7 -7 + 4v + 2v2 = 5 + -5 Combine like terms: 5 + -5 = 0 -7 + 4v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 2v + v2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 2v + 3.5 + v2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 2v + v2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 2v + v2 = 0 + 3.5 2v + v2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 2v + v2 = 3.5 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 = 3.5 + 1 Reorder the terms: 1 + 2v + v2 = 3.5 + 1 Combine like terms: 3.5 + 1 = 4.5 1 + 2v + v2 = 4.5 Factor a perfect square on the left side: (v + 1)(v + 1) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (v + 1) equal to 2.121320344 and -2.121320344.Subproblem 1
v + 1 = 2.121320344 Simplifying v + 1 = 2.121320344 Reorder the terms: 1 + v = 2.121320344 Solving 1 + v = 2.121320344 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 = 2.121320344 + -1 Combine like terms: 1 + -1 = 0 0 + v = 2.121320344 + -1 v = 2.121320344 + -1 Combine like terms: 2.121320344 + -1 = 1.121320344 v = 1.121320344 Simplifying v = 1.121320344Subproblem 2
v + 1 = -2.121320344 Simplifying v + 1 = -2.121320344 Reorder the terms: 1 + v = -2.121320344 Solving 1 + v = -2.121320344 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 = -2.121320344 + -1 Combine like terms: 1 + -1 = 0 0 + v = -2.121320344 + -1 v = -2.121320344 + -1 Combine like terms: -2.121320344 + -1 = -3.121320344 v = -3.121320344 Simplifying v = -3.121320344Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.121320344, -3.121320344}
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