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Simplifying v2 + 9 = 2v2 + 4v + -6 Reorder the terms: 9 + v2 = 2v2 + 4v + -6 Reorder the terms: 9 + v2 = -6 + 4v + 2v2 Solving 9 + v2 = -6 + 4v + 2v2 Solving for variable 'v'. Reorder the terms: 9 + 6 + -4v + v2 + -2v2 = -6 + 4v + 2v2 + 6 + -4v + -2v2 Combine like terms: 9 + 6 = 15 15 + -4v + v2 + -2v2 = -6 + 4v + 2v2 + 6 + -4v + -2v2 Combine like terms: v2 + -2v2 = -1v2 15 + -4v + -1v2 = -6 + 4v + 2v2 + 6 + -4v + -2v2 Reorder the terms: 15 + -4v + -1v2 = -6 + 6 + 4v + -4v + 2v2 + -2v2 Combine like terms: -6 + 6 = 0 15 + -4v + -1v2 = 0 + 4v + -4v + 2v2 + -2v2 15 + -4v + -1v2 = 4v + -4v + 2v2 + -2v2 Combine like terms: 4v + -4v = 0 15 + -4v + -1v2 = 0 + 2v2 + -2v2 15 + -4v + -1v2 = 2v2 + -2v2 Combine like terms: 2v2 + -2v2 = 0 15 + -4v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + 4v + v2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 4v + 15 + v2 = 0 + 15 Reorder the terms: -15 + 15 + 4v + v2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 4v + v2 = 0 + 15 4v + v2 = 0 + 15 Combine like terms: 0 + 15 = 15 4v + v2 = 15 The v term is 4v. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4v + 4 + v2 = 15 + 4 Reorder the terms: 4 + 4v + v2 = 15 + 4 Combine like terms: 15 + 4 = 19 4 + 4v + v2 = 19 Factor a perfect square on the left side: (v + 2)(v + 2) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (v + 2) equal to 4.358898944 and -4.358898944.Subproblem 1
v + 2 = 4.358898944 Simplifying v + 2 = 4.358898944 Reorder the terms: 2 + v = 4.358898944 Solving 2 + v = 4.358898944 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = 4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + v = 4.358898944 + -2 v = 4.358898944 + -2 Combine like terms: 4.358898944 + -2 = 2.358898944 v = 2.358898944 Simplifying v = 2.358898944Subproblem 2
v + 2 = -4.358898944 Simplifying v + 2 = -4.358898944 Reorder the terms: 2 + v = -4.358898944 Solving 2 + v = -4.358898944 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = -4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + v = -4.358898944 + -2 v = -4.358898944 + -2 Combine like terms: -4.358898944 + -2 = -6.358898944 v = -6.358898944 Simplifying v = -6.358898944Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.358898944, -6.358898944}
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