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Simplifying 9v2 + -13v + 3 = 0 Reorder the terms: 3 + -13v + 9v2 = 0 Solving 3 + -13v + 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'. 0.3333333333 + -1.444444444v + v2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -1.444444444v + -0.3333333333 + v2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -1.444444444v + v2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -1.444444444v + v2 = 0 + -0.3333333333 -1.444444444v + v2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -1.444444444v + v2 = -0.3333333333 The v term is -1.444444444v. Take half its coefficient (-0.722222222). Square it (0.5216049380) and add it to both sides. Add '0.5216049380' to each side of the equation. -1.444444444v + 0.5216049380 + v2 = -0.3333333333 + 0.5216049380 Reorder the terms: 0.5216049380 + -1.444444444v + v2 = -0.3333333333 + 0.5216049380 Combine like terms: -0.3333333333 + 0.5216049380 = 0.1882716047 0.5216049380 + -1.444444444v + v2 = 0.1882716047 Factor a perfect square on the left side: (v + -0.722222222)(v + -0.722222222) = 0.1882716047 Calculate the square root of the right side: 0.433902759 Break this problem into two subproblems by setting (v + -0.722222222) equal to 0.433902759 and -0.433902759.Subproblem 1
v + -0.722222222 = 0.433902759 Simplifying v + -0.722222222 = 0.433902759 Reorder the terms: -0.722222222 + v = 0.433902759 Solving -0.722222222 + v = 0.433902759 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + v = 0.433902759 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + v = 0.433902759 + 0.722222222 v = 0.433902759 + 0.722222222 Combine like terms: 0.433902759 + 0.722222222 = 1.156124981 v = 1.156124981 Simplifying v = 1.156124981Subproblem 2
v + -0.722222222 = -0.433902759 Simplifying v + -0.722222222 = -0.433902759 Reorder the terms: -0.722222222 + v = -0.433902759 Solving -0.722222222 + v = -0.433902759 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + v = -0.433902759 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + v = -0.433902759 + 0.722222222 v = -0.433902759 + 0.722222222 Combine like terms: -0.433902759 + 0.722222222 = 0.288319463 v = 0.288319463 Simplifying v = 0.288319463Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.156124981, 0.288319463}
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