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Simplifying 5v2 + -31v + -20 = 0 Reorder the terms: -20 + -31v + 5v2 = 0 Solving -20 + -31v + 5v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + -6.2v + v2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -6.2v + 4 + v2 = 0 + 4 Reorder the terms: -4 + 4 + -6.2v + v2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -6.2v + v2 = 0 + 4 -6.2v + v2 = 0 + 4 Combine like terms: 0 + 4 = 4 -6.2v + v2 = 4 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 = 4 + 9.61 Reorder the terms: 9.61 + -6.2v + v2 = 4 + 9.61 Combine like terms: 4 + 9.61 = 13.61 9.61 + -6.2v + v2 = 13.61 Factor a perfect square on the left side: (v + -3.1)(v + -3.1) = 13.61 Calculate the square root of the right side: 3.689173349 Break this problem into two subproblems by setting (v + -3.1) equal to 3.689173349 and -3.689173349.Subproblem 1
v + -3.1 = 3.689173349 Simplifying v + -3.1 = 3.689173349 Reorder the terms: -3.1 + v = 3.689173349 Solving -3.1 + v = 3.689173349 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 = 3.689173349 + 3.1 Combine like terms: -3.1 + 3.1 = 0.0 0.0 + v = 3.689173349 + 3.1 v = 3.689173349 + 3.1 Combine like terms: 3.689173349 + 3.1 = 6.789173349 v = 6.789173349 Simplifying v = 6.789173349Subproblem 2
v + -3.1 = -3.689173349 Simplifying v + -3.1 = -3.689173349 Reorder the terms: -3.1 + v = -3.689173349 Solving -3.1 + v = -3.689173349 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 = -3.689173349 + 3.1 Combine like terms: -3.1 + 3.1 = 0.0 0.0 + v = -3.689173349 + 3.1 v = -3.689173349 + 3.1 Combine like terms: -3.689173349 + 3.1 = -0.589173349 v = -0.589173349 Simplifying v = -0.589173349Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.789173349, -0.589173349}
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