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Simplifying 9v2 + 5v + -9 = 0 Reorder the terms: -9 + 5v + 9v2 = 0 Solving -9 + 5v + 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'. -1 + 0.5555555556v + v2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.5555555556v + 1 + v2 = 0 + 1 Reorder the terms: -1 + 1 + 0.5555555556v + v2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.5555555556v + v2 = 0 + 1 0.5555555556v + v2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.5555555556v + v2 = 1 The v term is 0.5555555556v. Take half its coefficient (0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. 0.5555555556v + 0.07716049384 + v2 = 1 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556v + v2 = 1 + 0.07716049384 Combine like terms: 1 + 0.07716049384 = 1.07716049384 0.07716049384 + 0.5555555556v + v2 = 1.07716049384 Factor a perfect square on the left side: (v + 0.2777777778)(v + 0.2777777778) = 1.07716049384 Calculate the square root of the right side: 1.037863427 Break this problem into two subproblems by setting (v + 0.2777777778) equal to 1.037863427 and -1.037863427.Subproblem 1
v + 0.2777777778 = 1.037863427 Simplifying v + 0.2777777778 = 1.037863427 Reorder the terms: 0.2777777778 + v = 1.037863427 Solving 0.2777777778 + v = 1.037863427 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + v = 1.037863427 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + v = 1.037863427 + -0.2777777778 v = 1.037863427 + -0.2777777778 Combine like terms: 1.037863427 + -0.2777777778 = 0.7600856492 v = 0.7600856492 Simplifying v = 0.7600856492Subproblem 2
v + 0.2777777778 = -1.037863427 Simplifying v + 0.2777777778 = -1.037863427 Reorder the terms: 0.2777777778 + v = -1.037863427 Solving 0.2777777778 + v = -1.037863427 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + v = -1.037863427 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + v = -1.037863427 + -0.2777777778 v = -1.037863427 + -0.2777777778 Combine like terms: -1.037863427 + -0.2777777778 = -1.3156412048 v = -1.3156412048 Simplifying v = -1.3156412048Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.7600856492, -1.3156412048}
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