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Simplifying 9v2 + 10v = 18 Reorder the terms: 10v + 9v2 = 18 Solving 10v + 9v2 = 18 Solving for variable 'v'. Reorder the terms: -18 + 10v + 9v2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 10v + 9v2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2 + 1.111111111v + v2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.111111111v + 2 + v2 = 0 + 2 Reorder the terms: -2 + 2 + 1.111111111v + v2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.111111111v + v2 = 0 + 2 1.111111111v + v2 = 0 + 2 Combine like terms: 0 + 2 = 2 1.111111111v + v2 = 2 The v term is 1.111111111v. Take half its coefficient (0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. 1.111111111v + 0.3086419752 + v2 = 2 + 0.3086419752 Reorder the terms: 0.3086419752 + 1.111111111v + v2 = 2 + 0.3086419752 Combine like terms: 2 + 0.3086419752 = 2.3086419752 0.3086419752 + 1.111111111v + v2 = 2.3086419752 Factor a perfect square on the left side: (v + 0.5555555555)(v + 0.5555555555) = 2.3086419752 Calculate the square root of the right side: 1.519421592 Break this problem into two subproblems by setting (v + 0.5555555555) equal to 1.519421592 and -1.519421592.Subproblem 1
v + 0.5555555555 = 1.519421592 Simplifying v + 0.5555555555 = 1.519421592 Reorder the terms: 0.5555555555 + v = 1.519421592 Solving 0.5555555555 + v = 1.519421592 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + v = 1.519421592 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + v = 1.519421592 + -0.5555555555 v = 1.519421592 + -0.5555555555 Combine like terms: 1.519421592 + -0.5555555555 = 0.9638660365 v = 0.9638660365 Simplifying v = 0.9638660365Subproblem 2
v + 0.5555555555 = -1.519421592 Simplifying v + 0.5555555555 = -1.519421592 Reorder the terms: 0.5555555555 + v = -1.519421592 Solving 0.5555555555 + v = -1.519421592 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + v = -1.519421592 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + v = -1.519421592 + -0.5555555555 v = -1.519421592 + -0.5555555555 Combine like terms: -1.519421592 + -0.5555555555 = -2.0749771475 v = -2.0749771475 Simplifying v = -2.0749771475Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.9638660365, -2.0749771475}
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