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Simplifying 19v2 + 6v + -6 = 0 Reorder the terms: -6 + 6v + 19v2 = 0 Solving -6 + 6v + 19v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -0.3157894737 + 0.3157894737v + v2 = 0 Move the constant term to the right: Add '0.3157894737' to each side of the equation. -0.3157894737 + 0.3157894737v + 0.3157894737 + v2 = 0 + 0.3157894737 Reorder the terms: -0.3157894737 + 0.3157894737 + 0.3157894737v + v2 = 0 + 0.3157894737 Combine like terms: -0.3157894737 + 0.3157894737 = 0.0000000000 0.0000000000 + 0.3157894737v + v2 = 0 + 0.3157894737 0.3157894737v + v2 = 0 + 0.3157894737 Combine like terms: 0 + 0.3157894737 = 0.3157894737 0.3157894737v + v2 = 0.3157894737 The v term is 0.3157894737v. Take half its coefficient (0.1578947369). Square it (0.02493074794) and add it to both sides. Add '0.02493074794' to each side of the equation. 0.3157894737v + 0.02493074794 + v2 = 0.3157894737 + 0.02493074794 Reorder the terms: 0.02493074794 + 0.3157894737v + v2 = 0.3157894737 + 0.02493074794 Combine like terms: 0.3157894737 + 0.02493074794 = 0.34072022164 0.02493074794 + 0.3157894737v + v2 = 0.34072022164 Factor a perfect square on the left side: (v + 0.1578947369)(v + 0.1578947369) = 0.34072022164 Calculate the square root of the right side: 0.583712448 Break this problem into two subproblems by setting (v + 0.1578947369) equal to 0.583712448 and -0.583712448.Subproblem 1
v + 0.1578947369 = 0.583712448 Simplifying v + 0.1578947369 = 0.583712448 Reorder the terms: 0.1578947369 + v = 0.583712448 Solving 0.1578947369 + v = 0.583712448 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.1578947369' to each side of the equation. 0.1578947369 + -0.1578947369 + v = 0.583712448 + -0.1578947369 Combine like terms: 0.1578947369 + -0.1578947369 = 0.0000000000 0.0000000000 + v = 0.583712448 + -0.1578947369 v = 0.583712448 + -0.1578947369 Combine like terms: 0.583712448 + -0.1578947369 = 0.4258177111 v = 0.4258177111 Simplifying v = 0.4258177111Subproblem 2
v + 0.1578947369 = -0.583712448 Simplifying v + 0.1578947369 = -0.583712448 Reorder the terms: 0.1578947369 + v = -0.583712448 Solving 0.1578947369 + v = -0.583712448 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.1578947369' to each side of the equation. 0.1578947369 + -0.1578947369 + v = -0.583712448 + -0.1578947369 Combine like terms: 0.1578947369 + -0.1578947369 = 0.0000000000 0.0000000000 + v = -0.583712448 + -0.1578947369 v = -0.583712448 + -0.1578947369 Combine like terms: -0.583712448 + -0.1578947369 = -0.7416071849 v = -0.7416071849 Simplifying v = -0.7416071849Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.4258177111, -0.7416071849}
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