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Simplifying 9v2 + 25v + 12 = 0 Reorder the terms: 12 + 25v + 9v2 = 0 Solving 12 + 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'. 1.333333333 + 2.777777778v + v2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 2.777777778v + -1.333333333 + v2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 2.777777778v + v2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 2.777777778v + v2 = 0 + -1.333333333 2.777777778v + v2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 2.777777778v + v2 = -1.333333333 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 = -1.333333333 + 1.929012346 Reorder the terms: 1.929012346 + 2.777777778v + v2 = -1.333333333 + 1.929012346 Combine like terms: -1.333333333 + 1.929012346 = 0.595679013 1.929012346 + 2.777777778v + v2 = 0.595679013 Factor a perfect square on the left side: (v + 1.388888889)(v + 1.388888889) = 0.595679013 Calculate the square root of the right side: 0.771802444 Break this problem into two subproblems by setting (v + 1.388888889) equal to 0.771802444 and -0.771802444.Subproblem 1
v + 1.388888889 = 0.771802444 Simplifying v + 1.388888889 = 0.771802444 Reorder the terms: 1.388888889 + v = 0.771802444 Solving 1.388888889 + v = 0.771802444 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 = 0.771802444 + -1.388888889 Combine like terms: 1.388888889 + -1.388888889 = 0.000000000 0.000000000 + v = 0.771802444 + -1.388888889 v = 0.771802444 + -1.388888889 Combine like terms: 0.771802444 + -1.388888889 = -0.617086445 v = -0.617086445 Simplifying v = -0.617086445Subproblem 2
v + 1.388888889 = -0.771802444 Simplifying v + 1.388888889 = -0.771802444 Reorder the terms: 1.388888889 + v = -0.771802444 Solving 1.388888889 + v = -0.771802444 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 = -0.771802444 + -1.388888889 Combine like terms: 1.388888889 + -1.388888889 = 0.000000000 0.000000000 + v = -0.771802444 + -1.388888889 v = -0.771802444 + -1.388888889 Combine like terms: -0.771802444 + -1.388888889 = -2.160691333 v = -2.160691333 Simplifying v = -2.160691333Solution
The solution to the problem is based on the solutions from the subproblems. v = {-0.617086445, -2.160691333}
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