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Simplifying 2v2 + -9v + 2 = 0 Reorder the terms: 2 + -9v + 2v2 = 0 Solving 2 + -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'. 1 + -4.5v + v2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4.5v + -1 + v2 = 0 + -1 Reorder the terms: 1 + -1 + -4.5v + v2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4.5v + v2 = 0 + -1 -4.5v + v2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4.5v + v2 = -1 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 = -1 + 5.0625 Reorder the terms: 5.0625 + -4.5v + v2 = -1 + 5.0625 Combine like terms: -1 + 5.0625 = 4.0625 5.0625 + -4.5v + v2 = 4.0625 Factor a perfect square on the left side: (v + -2.25)(v + -2.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (v + -2.25) equal to 2.015564437 and -2.015564437.Subproblem 1
v + -2.25 = 2.015564437 Simplifying v + -2.25 = 2.015564437 Reorder the terms: -2.25 + v = 2.015564437 Solving -2.25 + v = 2.015564437 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 = 2.015564437 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + v = 2.015564437 + 2.25 v = 2.015564437 + 2.25 Combine like terms: 2.015564437 + 2.25 = 4.265564437 v = 4.265564437 Simplifying v = 4.265564437Subproblem 2
v + -2.25 = -2.015564437 Simplifying v + -2.25 = -2.015564437 Reorder the terms: -2.25 + v = -2.015564437 Solving -2.25 + v = -2.015564437 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 = -2.015564437 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + v = -2.015564437 + 2.25 v = -2.015564437 + 2.25 Combine like terms: -2.015564437 + 2.25 = 0.234435563 v = 0.234435563 Simplifying v = 0.234435563Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.265564437, 0.234435563}
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