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Simplifying v(6v2 + 17v + 2) = 0 Reorder the terms: v(2 + 17v + 6v2) = 0 (2 * v + 17v * v + 6v2 * v) = 0 (2v + 17v2 + 6v3) = 0 Solving 2v + 17v2 + 6v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), 'v'. v(2 + 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 '(2 + 17v + 6v2)' equal to zero and attempt to solve: Simplifying 2 + 17v + 6v2 = 0 Solving 2 + 17v + 6v2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.3333333333 + 2.833333333v + v2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 2.833333333v + -0.3333333333 + v2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 2.833333333v + v2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 2.833333333v + v2 = 0 + -0.3333333333 2.833333333v + v2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 2.833333333v + v2 = -0.3333333333 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 = -0.3333333333 + 2.006944445 Reorder the terms: 2.006944445 + 2.833333333v + v2 = -0.3333333333 + 2.006944445 Combine like terms: -0.3333333333 + 2.006944445 = 1.6736111117 2.006944445 + 2.833333333v + v2 = 1.6736111117 Factor a perfect square on the left side: (v + 1.416666667)(v + 1.416666667) = 1.6736111117 Calculate the square root of the right side: 1.293681225 Break this problem into two subproblems by setting (v + 1.416666667) equal to 1.293681225 and -1.293681225.Subproblem 1
v + 1.416666667 = 1.293681225 Simplifying v + 1.416666667 = 1.293681225 Reorder the terms: 1.416666667 + v = 1.293681225 Solving 1.416666667 + v = 1.293681225 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 = 1.293681225 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + v = 1.293681225 + -1.416666667 v = 1.293681225 + -1.416666667 Combine like terms: 1.293681225 + -1.416666667 = -0.122985442 v = -0.122985442 Simplifying v = -0.122985442Subproblem 2
v + 1.416666667 = -1.293681225 Simplifying v + 1.416666667 = -1.293681225 Reorder the terms: 1.416666667 + v = -1.293681225 Solving 1.416666667 + v = -1.293681225 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 = -1.293681225 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + v = -1.293681225 + -1.416666667 v = -1.293681225 + -1.416666667 Combine like terms: -1.293681225 + -1.416666667 = -2.710347892 v = -2.710347892 Simplifying v = -2.710347892Solution
The solution to the problem is based on the solutions from the subproblems. v = {-0.122985442, -2.710347892}Solution
v = {0, -0.122985442, -2.710347892}
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