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Simplifying 9v2 + -18v = -7 Reorder the terms: -18v + 9v2 = -7 Solving -18v + 9v2 = -7 Solving for variable 'v'. Reorder the terms: 7 + -18v + 9v2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + -18v + 9v2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.7777777778 + -2v + v2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + -2v + -0.7777777778 + v2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + -2v + v2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + -2v + v2 = 0 + -0.7777777778 -2v + v2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 -2v + v2 = -0.7777777778 The v term is -2v. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2v + 1 + v2 = -0.7777777778 + 1 Reorder the terms: 1 + -2v + v2 = -0.7777777778 + 1 Combine like terms: -0.7777777778 + 1 = 0.2222222222 1 + -2v + v2 = 0.2222222222 Factor a perfect square on the left side: (v + -1)(v + -1) = 0.2222222222 Calculate the square root of the right side: 0.471404521 Break this problem into two subproblems by setting (v + -1) equal to 0.471404521 and -0.471404521.Subproblem 1
v + -1 = 0.471404521 Simplifying v + -1 = 0.471404521 Reorder the terms: -1 + v = 0.471404521 Solving -1 + v = 0.471404521 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + v = 0.471404521 + 1 Combine like terms: -1 + 1 = 0 0 + v = 0.471404521 + 1 v = 0.471404521 + 1 Combine like terms: 0.471404521 + 1 = 1.471404521 v = 1.471404521 Simplifying v = 1.471404521Subproblem 2
v + -1 = -0.471404521 Simplifying v + -1 = -0.471404521 Reorder the terms: -1 + v = -0.471404521 Solving -1 + v = -0.471404521 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + v = -0.471404521 + 1 Combine like terms: -1 + 1 = 0 0 + v = -0.471404521 + 1 v = -0.471404521 + 1 Combine like terms: -0.471404521 + 1 = 0.528595479 v = 0.528595479 Simplifying v = 0.528595479Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.471404521, 0.528595479}
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