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Simplifying (9v2 + 3v + -5) + (5v2 + -3v) + -1(9v2 + 4v + -1) = 0 Reorder the terms: (-5 + 3v + 9v2) + (5v2 + -3v) + -1(9v2 + 4v + -1) = 0 Remove parenthesis around (-5 + 3v + 9v2) -5 + 3v + 9v2 + (5v2 + -3v) + -1(9v2 + 4v + -1) = 0 Reorder the terms: -5 + 3v + 9v2 + (-3v + 5v2) + -1(9v2 + 4v + -1) = 0 Remove parenthesis around (-3v + 5v2) -5 + 3v + 9v2 + -3v + 5v2 + -1(9v2 + 4v + -1) = 0 Reorder the terms: -5 + 3v + 9v2 + -3v + 5v2 + -1(-1 + 4v + 9v2) = 0 -5 + 3v + 9v2 + -3v + 5v2 + (-1 * -1 + 4v * -1 + 9v2 * -1) = 0 -5 + 3v + 9v2 + -3v + 5v2 + (1 + -4v + -9v2) = 0 Reorder the terms: -5 + 1 + 3v + -3v + -4v + 9v2 + 5v2 + -9v2 = 0 Combine like terms: -5 + 1 = -4 -4 + 3v + -3v + -4v + 9v2 + 5v2 + -9v2 = 0 Combine like terms: 3v + -3v = 0 -4 + 0 + -4v + 9v2 + 5v2 + -9v2 = 0 -4 + -4v + 9v2 + 5v2 + -9v2 = 0 Combine like terms: 9v2 + 5v2 = 14v2 -4 + -4v + 14v2 + -9v2 = 0 Combine like terms: 14v2 + -9v2 = 5v2 -4 + -4v + 5v2 = 0 Solving -4 + -4v + 5v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -0.8v + v2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -0.8v + 0.8 + v2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -0.8v + v2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -0.8v + v2 = 0 + 0.8 -0.8v + v2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -0.8v + v2 = 0.8 The v term is -0.8v. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8v + 0.16 + v2 = 0.8 + 0.16 Reorder the terms: 0.16 + -0.8v + v2 = 0.8 + 0.16 Combine like terms: 0.8 + 0.16 = 0.96 0.16 + -0.8v + v2 = 0.96 Factor a perfect square on the left side: (v + -0.4)(v + -0.4) = 0.96 Calculate the square root of the right side: 0.979795897 Break this problem into two subproblems by setting (v + -0.4) equal to 0.979795897 and -0.979795897.Subproblem 1
v + -0.4 = 0.979795897 Simplifying v + -0.4 = 0.979795897 Reorder the terms: -0.4 + v = 0.979795897 Solving -0.4 + v = 0.979795897 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + v = 0.979795897 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + v = 0.979795897 + 0.4 v = 0.979795897 + 0.4 Combine like terms: 0.979795897 + 0.4 = 1.379795897 v = 1.379795897 Simplifying v = 1.379795897Subproblem 2
v + -0.4 = -0.979795897 Simplifying v + -0.4 = -0.979795897 Reorder the terms: -0.4 + v = -0.979795897 Solving -0.4 + v = -0.979795897 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + v = -0.979795897 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + v = -0.979795897 + 0.4 v = -0.979795897 + 0.4 Combine like terms: -0.979795897 + 0.4 = -0.579795897 v = -0.579795897 Simplifying v = -0.579795897Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.379795897, -0.579795897}
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