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Simplifying 0 = 4v2 + 9v + -8 Reorder the terms: 0 = -8 + 9v + 4v2 Solving 0 = -8 + 9v + 4v2 Solving for variable 'v'. Combine like terms: 0 + 8 = 8 8 + -9v + -4v2 = -8 + 9v + 4v2 + 8 + -9v + -4v2 Reorder the terms: 8 + -9v + -4v2 = -8 + 8 + 9v + -9v + 4v2 + -4v2 Combine like terms: -8 + 8 = 0 8 + -9v + -4v2 = 0 + 9v + -9v + 4v2 + -4v2 8 + -9v + -4v2 = 9v + -9v + 4v2 + -4v2 Combine like terms: 9v + -9v = 0 8 + -9v + -4v2 = 0 + 4v2 + -4v2 8 + -9v + -4v2 = 4v2 + -4v2 Combine like terms: 4v2 + -4v2 = 0 8 + -9v + -4v2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2 + 2.25v + v2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 2.25v + 2 + v2 = 0 + 2 Reorder the terms: -2 + 2 + 2.25v + v2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2.25v + v2 = 0 + 2 2.25v + v2 = 0 + 2 Combine like terms: 0 + 2 = 2 2.25v + v2 = 2 The v term is 2.25v. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25v + 1.265625 + v2 = 2 + 1.265625 Reorder the terms: 1.265625 + 2.25v + v2 = 2 + 1.265625 Combine like terms: 2 + 1.265625 = 3.265625 1.265625 + 2.25v + v2 = 3.265625 Factor a perfect square on the left side: (v + 1.125)(v + 1.125) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (v + 1.125) equal to 1.807104037 and -1.807104037.Subproblem 1
v + 1.125 = 1.807104037 Simplifying v + 1.125 = 1.807104037 Reorder the terms: 1.125 + v = 1.807104037 Solving 1.125 + v = 1.807104037 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + v = 1.807104037 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + v = 1.807104037 + -1.125 v = 1.807104037 + -1.125 Combine like terms: 1.807104037 + -1.125 = 0.682104037 v = 0.682104037 Simplifying v = 0.682104037Subproblem 2
v + 1.125 = -1.807104037 Simplifying v + 1.125 = -1.807104037 Reorder the terms: 1.125 + v = -1.807104037 Solving 1.125 + v = -1.807104037 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + v = -1.807104037 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + v = -1.807104037 + -1.125 v = -1.807104037 + -1.125 Combine like terms: -1.807104037 + -1.125 = -2.932104037 v = -2.932104037 Simplifying v = -2.932104037Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.682104037, -2.932104037}
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