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Simplifying 9v2 + -4v + -9 = 0 Reorder the terms: -9 + -4v + 9v2 = 0 Solving -9 + -4v + 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 + -0.4444444444v + v2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.4444444444v + 1 + v2 = 0 + 1 Reorder the terms: -1 + 1 + -0.4444444444v + v2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.4444444444v + v2 = 0 + 1 -0.4444444444v + v2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.4444444444v + v2 = 1 The v term is -0.4444444444v. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444v + 0.04938271604 + v2 = 1 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444v + v2 = 1 + 0.04938271604 Combine like terms: 1 + 0.04938271604 = 1.04938271604 0.04938271604 + -0.4444444444v + v2 = 1.04938271604 Factor a perfect square on the left side: (v + -0.2222222222)(v + -0.2222222222) = 1.04938271604 Calculate the square root of the right side: 1.024393829 Break this problem into two subproblems by setting (v + -0.2222222222) equal to 1.024393829 and -1.024393829.Subproblem 1
v + -0.2222222222 = 1.024393829 Simplifying v + -0.2222222222 = 1.024393829 Reorder the terms: -0.2222222222 + v = 1.024393829 Solving -0.2222222222 + v = 1.024393829 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + v = 1.024393829 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + v = 1.024393829 + 0.2222222222 v = 1.024393829 + 0.2222222222 Combine like terms: 1.024393829 + 0.2222222222 = 1.2466160512 v = 1.2466160512 Simplifying v = 1.2466160512Subproblem 2
v + -0.2222222222 = -1.024393829 Simplifying v + -0.2222222222 = -1.024393829 Reorder the terms: -0.2222222222 + v = -1.024393829 Solving -0.2222222222 + v = -1.024393829 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + v = -1.024393829 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + v = -1.024393829 + 0.2222222222 v = -1.024393829 + 0.2222222222 Combine like terms: -1.024393829 + 0.2222222222 = -0.8021716068 v = -0.8021716068 Simplifying v = -0.8021716068Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.2466160512, -0.8021716068}
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