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Simplifying 2v2 + -9v + 8 = 0 Reorder the terms: 8 + -9v + 2v2 = 0 Solving 8 + -9v + 2v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + -4.5v + v2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -4.5v + -4 + v2 = 0 + -4 Reorder the terms: 4 + -4 + -4.5v + v2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -4.5v + v2 = 0 + -4 -4.5v + v2 = 0 + -4 Combine like terms: 0 + -4 = -4 -4.5v + v2 = -4 The v term is -4.5v. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5v + 5.0625 + v2 = -4 + 5.0625 Reorder the terms: 5.0625 + -4.5v + v2 = -4 + 5.0625 Combine like terms: -4 + 5.0625 = 1.0625 5.0625 + -4.5v + v2 = 1.0625 Factor a perfect square on the left side: (v + -2.25)(v + -2.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (v + -2.25) equal to 1.030776406 and -1.030776406.Subproblem 1
v + -2.25 = 1.030776406 Simplifying v + -2.25 = 1.030776406 Reorder the terms: -2.25 + v = 1.030776406 Solving -2.25 + v = 1.030776406 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + v = 1.030776406 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + v = 1.030776406 + 2.25 v = 1.030776406 + 2.25 Combine like terms: 1.030776406 + 2.25 = 3.280776406 v = 3.280776406 Simplifying v = 3.280776406Subproblem 2
v + -2.25 = -1.030776406 Simplifying v + -2.25 = -1.030776406 Reorder the terms: -2.25 + v = -1.030776406 Solving -2.25 + v = -1.030776406 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + v = -1.030776406 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + v = -1.030776406 + 2.25 v = -1.030776406 + 2.25 Combine like terms: -1.030776406 + 2.25 = 1.219223594 v = 1.219223594 Simplifying v = 1.219223594Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.280776406, 1.219223594}
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