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Simplifying 9v2 + 3v + -17 = 0 Reorder the terms: -17 + 3v + 9v2 = 0 Solving -17 + 3v + 9v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.888888889 + 0.3333333333v + v2 = 0 Move the constant term to the right: Add '1.888888889' to each side of the equation. -1.888888889 + 0.3333333333v + 1.888888889 + v2 = 0 + 1.888888889 Reorder the terms: -1.888888889 + 1.888888889 + 0.3333333333v + v2 = 0 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + 0.3333333333v + v2 = 0 + 1.888888889 0.3333333333v + v2 = 0 + 1.888888889 Combine like terms: 0 + 1.888888889 = 1.888888889 0.3333333333v + v2 = 1.888888889 The v term is 0.3333333333v. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333v + 0.02777777779 + v2 = 1.888888889 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333v + v2 = 1.888888889 + 0.02777777779 Combine like terms: 1.888888889 + 0.02777777779 = 1.91666666679 0.02777777779 + 0.3333333333v + v2 = 1.91666666679 Factor a perfect square on the left side: (v + 0.1666666667)(v + 0.1666666667) = 1.91666666679 Calculate the square root of the right side: 1.384437311 Break this problem into two subproblems by setting (v + 0.1666666667) equal to 1.384437311 and -1.384437311.Subproblem 1
v + 0.1666666667 = 1.384437311 Simplifying v + 0.1666666667 = 1.384437311 Reorder the terms: 0.1666666667 + v = 1.384437311 Solving 0.1666666667 + v = 1.384437311 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + v = 1.384437311 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + v = 1.384437311 + -0.1666666667 v = 1.384437311 + -0.1666666667 Combine like terms: 1.384437311 + -0.1666666667 = 1.2177706443 v = 1.2177706443 Simplifying v = 1.2177706443Subproblem 2
v + 0.1666666667 = -1.384437311 Simplifying v + 0.1666666667 = -1.384437311 Reorder the terms: 0.1666666667 + v = -1.384437311 Solving 0.1666666667 + v = -1.384437311 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + v = -1.384437311 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + v = -1.384437311 + -0.1666666667 v = -1.384437311 + -0.1666666667 Combine like terms: -1.384437311 + -0.1666666667 = -1.5511039777 v = -1.5511039777 Simplifying v = -1.5511039777Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.2177706443, -1.5511039777}
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