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Simplifying -1v2 + 4v + 8 = 0 Reorder the terms: 8 + 4v + -1v2 = 0 Solving 8 + 4v + -1v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + -4v + v2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -4v + 8 + v2 = 0 + 8 Reorder the terms: -8 + 8 + -4v + v2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -4v + v2 = 0 + 8 -4v + v2 = 0 + 8 Combine like terms: 0 + 8 = 8 -4v + v2 = 8 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 = 8 + 4 Reorder the terms: 4 + -4v + v2 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + -4v + v2 = 12 Factor a perfect square on the left side: (v + -2)(v + -2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (v + -2) equal to 3.464101615 and -3.464101615.Subproblem 1
v + -2 = 3.464101615 Simplifying v + -2 = 3.464101615 Reorder the terms: -2 + v = 3.464101615 Solving -2 + v = 3.464101615 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 = 3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + v = 3.464101615 + 2 v = 3.464101615 + 2 Combine like terms: 3.464101615 + 2 = 5.464101615 v = 5.464101615 Simplifying v = 5.464101615Subproblem 2
v + -2 = -3.464101615 Simplifying v + -2 = -3.464101615 Reorder the terms: -2 + v = -3.464101615 Solving -2 + v = -3.464101615 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 = -3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + v = -3.464101615 + 2 v = -3.464101615 + 2 Combine like terms: -3.464101615 + 2 = -1.464101615 v = -1.464101615 Simplifying v = -1.464101615Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.464101615, -1.464101615}
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