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Simplifying 4v2 + 8v + -39 = 0 Reorder the terms: -39 + 8v + 4v2 = 0 Solving -39 + 8v + 4v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9.75 + 2v + v2 = 0 Move the constant term to the right: Add '9.75' to each side of the equation. -9.75 + 2v + 9.75 + v2 = 0 + 9.75 Reorder the terms: -9.75 + 9.75 + 2v + v2 = 0 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + 2v + v2 = 0 + 9.75 2v + v2 = 0 + 9.75 Combine like terms: 0 + 9.75 = 9.75 2v + v2 = 9.75 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 = 9.75 + 1 Reorder the terms: 1 + 2v + v2 = 9.75 + 1 Combine like terms: 9.75 + 1 = 10.75 1 + 2v + v2 = 10.75 Factor a perfect square on the left side: (v + 1)(v + 1) = 10.75 Calculate the square root of the right side: 3.278719262 Break this problem into two subproblems by setting (v + 1) equal to 3.278719262 and -3.278719262.Subproblem 1
v + 1 = 3.278719262 Simplifying v + 1 = 3.278719262 Reorder the terms: 1 + v = 3.278719262 Solving 1 + v = 3.278719262 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 = 3.278719262 + -1 Combine like terms: 1 + -1 = 0 0 + v = 3.278719262 + -1 v = 3.278719262 + -1 Combine like terms: 3.278719262 + -1 = 2.278719262 v = 2.278719262 Simplifying v = 2.278719262Subproblem 2
v + 1 = -3.278719262 Simplifying v + 1 = -3.278719262 Reorder the terms: 1 + v = -3.278719262 Solving 1 + v = -3.278719262 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 = -3.278719262 + -1 Combine like terms: 1 + -1 = 0 0 + v = -3.278719262 + -1 v = -3.278719262 + -1 Combine like terms: -3.278719262 + -1 = -4.278719262 v = -4.278719262 Simplifying v = -4.278719262Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.278719262, -4.278719262}
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