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Simplifying 5v2 = -31v + -28 Reorder the terms: 5v2 = -28 + -31v Solving 5v2 = -28 + -31v Solving for variable 'v'. Reorder the terms: 28 + 31v + 5v2 = -28 + -31v + 28 + 31v Reorder the terms: 28 + 31v + 5v2 = -28 + 28 + -31v + 31v Combine like terms: -28 + 28 = 0 28 + 31v + 5v2 = 0 + -31v + 31v 28 + 31v + 5v2 = -31v + 31v Combine like terms: -31v + 31v = 0 28 + 31v + 5v2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5.6 + 6.2v + v2 = 0 Move the constant term to the right: Add '-5.6' to each side of the equation. 5.6 + 6.2v + -5.6 + v2 = 0 + -5.6 Reorder the terms: 5.6 + -5.6 + 6.2v + v2 = 0 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + 6.2v + v2 = 0 + -5.6 6.2v + v2 = 0 + -5.6 Combine like terms: 0 + -5.6 = -5.6 6.2v + v2 = -5.6 The v term is 6.2v. Take half its coefficient (3.1). Square it (9.61) and add it to both sides. Add '9.61' to each side of the equation. 6.2v + 9.61 + v2 = -5.6 + 9.61 Reorder the terms: 9.61 + 6.2v + v2 = -5.6 + 9.61 Combine like terms: -5.6 + 9.61 = 4.01 9.61 + 6.2v + v2 = 4.01 Factor a perfect square on the left side: (v + 3.1)(v + 3.1) = 4.01 Calculate the square root of the right side: 2.002498439 Break this problem into two subproblems by setting (v + 3.1) equal to 2.002498439 and -2.002498439.Subproblem 1
v + 3.1 = 2.002498439 Simplifying v + 3.1 = 2.002498439 Reorder the terms: 3.1 + v = 2.002498439 Solving 3.1 + v = 2.002498439 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.1' to each side of the equation. 3.1 + -3.1 + v = 2.002498439 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + v = 2.002498439 + -3.1 v = 2.002498439 + -3.1 Combine like terms: 2.002498439 + -3.1 = -1.097501561 v = -1.097501561 Simplifying v = -1.097501561Subproblem 2
v + 3.1 = -2.002498439 Simplifying v + 3.1 = -2.002498439 Reorder the terms: 3.1 + v = -2.002498439 Solving 3.1 + v = -2.002498439 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.1' to each side of the equation. 3.1 + -3.1 + v = -2.002498439 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + v = -2.002498439 + -3.1 v = -2.002498439 + -3.1 Combine like terms: -2.002498439 + -3.1 = -5.102498439 v = -5.102498439 Simplifying v = -5.102498439Solution
The solution to the problem is based on the solutions from the subproblems. v = {-1.097501561, -5.102498439}
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