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Simplifying -9v2 + 25v + 30 = 0 Reorder the terms: 30 + 25v + -9v2 = 0 Solving 30 + 25v + -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'. -3.333333333 + -2.777777778v + v2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -2.777777778v + 3.333333333 + v2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -2.777777778v + v2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -2.777777778v + v2 = 0 + 3.333333333 -2.777777778v + v2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -2.777777778v + v2 = 3.333333333 The v term is -2.777777778v. Take half its coefficient (-1.388888889). Square it (1.929012346) and add it to both sides. Add '1.929012346' to each side of the equation. -2.777777778v + 1.929012346 + v2 = 3.333333333 + 1.929012346 Reorder the terms: 1.929012346 + -2.777777778v + v2 = 3.333333333 + 1.929012346 Combine like terms: 3.333333333 + 1.929012346 = 5.262345679 1.929012346 + -2.777777778v + v2 = 5.262345679 Factor a perfect square on the left side: (v + -1.388888889)(v + -1.388888889) = 5.262345679 Calculate the square root of the right side: 2.293980314 Break this problem into two subproblems by setting (v + -1.388888889) equal to 2.293980314 and -2.293980314.Subproblem 1
v + -1.388888889 = 2.293980314 Simplifying v + -1.388888889 = 2.293980314 Reorder the terms: -1.388888889 + v = 2.293980314 Solving -1.388888889 + v = 2.293980314 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + v = 2.293980314 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + v = 2.293980314 + 1.388888889 v = 2.293980314 + 1.388888889 Combine like terms: 2.293980314 + 1.388888889 = 3.682869203 v = 3.682869203 Simplifying v = 3.682869203Subproblem 2
v + -1.388888889 = -2.293980314 Simplifying v + -1.388888889 = -2.293980314 Reorder the terms: -1.388888889 + v = -2.293980314 Solving -1.388888889 + v = -2.293980314 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + v = -2.293980314 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + v = -2.293980314 + 1.388888889 v = -2.293980314 + 1.388888889 Combine like terms: -2.293980314 + 1.388888889 = -0.905091425 v = -0.905091425 Simplifying v = -0.905091425Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.682869203, -0.905091425}
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