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Simplifying 17v2 + 5v = 6v3 Reorder the terms: 5v + 17v2 = 6v3 Solving 5v + 17v2 = 6v3 Solving for variable 'v'. Combine like terms: 6v3 + -6v3 = 0 5v + 17v2 + -6v3 = 0 Factor out the Greatest Common Factor (GCF), 'v'. v(5 + 17v + -6v2) = 0Subproblem 1
Set the factor 'v' equal to zero and attempt to solve: Simplifying v = 0 Solving v = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v = 0Subproblem 2
Set the factor '(5 + 17v + -6v2)' equal to zero and attempt to solve: Simplifying 5 + 17v + -6v2 = 0 Solving 5 + 17v + -6v2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.8333333333 + -2.833333333v + v2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -2.833333333v + 0.8333333333 + v2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -2.833333333v + v2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -2.833333333v + v2 = 0 + 0.8333333333 -2.833333333v + v2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -2.833333333v + v2 = 0.8333333333 The v term is -2.833333333v. Take half its coefficient (-1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. -2.833333333v + 2.006944445 + v2 = 0.8333333333 + 2.006944445 Reorder the terms: 2.006944445 + -2.833333333v + v2 = 0.8333333333 + 2.006944445 Combine like terms: 0.8333333333 + 2.006944445 = 2.8402777783 2.006944445 + -2.833333333v + v2 = 2.8402777783 Factor a perfect square on the left side: (v + -1.416666667)(v + -1.416666667) = 2.8402777783 Calculate the square root of the right side: 1.685312368 Break this problem into two subproblems by setting (v + -1.416666667) equal to 1.685312368 and -1.685312368.Subproblem 1
v + -1.416666667 = 1.685312368 Simplifying v + -1.416666667 = 1.685312368 Reorder the terms: -1.416666667 + v = 1.685312368 Solving -1.416666667 + v = 1.685312368 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + v = 1.685312368 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + v = 1.685312368 + 1.416666667 v = 1.685312368 + 1.416666667 Combine like terms: 1.685312368 + 1.416666667 = 3.101979035 v = 3.101979035 Simplifying v = 3.101979035Subproblem 2
v + -1.416666667 = -1.685312368 Simplifying v + -1.416666667 = -1.685312368 Reorder the terms: -1.416666667 + v = -1.685312368 Solving -1.416666667 + v = -1.685312368 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + v = -1.685312368 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + v = -1.685312368 + 1.416666667 v = -1.685312368 + 1.416666667 Combine like terms: -1.685312368 + 1.416666667 = -0.268645701 v = -0.268645701 Simplifying v = -0.268645701Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.101979035, -0.268645701}Solution
v = {0, 3.101979035, -0.268645701}
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