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Simplifying 4v2 + -31v + 24 = 0 Reorder the terms: 24 + -31v + 4v2 = 0 Solving 24 + -31v + 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'. 6 + -7.75v + v2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -7.75v + -6 + v2 = 0 + -6 Reorder the terms: 6 + -6 + -7.75v + v2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7.75v + v2 = 0 + -6 -7.75v + v2 = 0 + -6 Combine like terms: 0 + -6 = -6 -7.75v + v2 = -6 The v term is -7.75v. Take half its coefficient (-3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. -7.75v + 15.015625 + v2 = -6 + 15.015625 Reorder the terms: 15.015625 + -7.75v + v2 = -6 + 15.015625 Combine like terms: -6 + 15.015625 = 9.015625 15.015625 + -7.75v + v2 = 9.015625 Factor a perfect square on the left side: (v + -3.875)(v + -3.875) = 9.015625 Calculate the square root of the right side: 3.002603037 Break this problem into two subproblems by setting (v + -3.875) equal to 3.002603037 and -3.002603037.Subproblem 1
v + -3.875 = 3.002603037 Simplifying v + -3.875 = 3.002603037 Reorder the terms: -3.875 + v = 3.002603037 Solving -3.875 + v = 3.002603037 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + v = 3.002603037 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + v = 3.002603037 + 3.875 v = 3.002603037 + 3.875 Combine like terms: 3.002603037 + 3.875 = 6.877603037 v = 6.877603037 Simplifying v = 6.877603037Subproblem 2
v + -3.875 = -3.002603037 Simplifying v + -3.875 = -3.002603037 Reorder the terms: -3.875 + v = -3.002603037 Solving -3.875 + v = -3.002603037 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + v = -3.002603037 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + v = -3.002603037 + 3.875 v = -3.002603037 + 3.875 Combine like terms: -3.002603037 + 3.875 = 0.872396963 v = 0.872396963 Simplifying v = 0.872396963Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.877603037, 0.872396963}
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