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Simplifying -9v(6 + v) + -2v = -10 (6 * -9v + v * -9v) + -2v = -10 (-54v + -9v2) + -2v = -10 Reorder the terms: -54v + -2v + -9v2 = -10 Combine like terms: -54v + -2v = -56v -56v + -9v2 = -10 Solving -56v + -9v2 = -10 Solving for variable 'v'. Reorder the terms: 10 + -56v + -9v2 = -10 + 10 Combine like terms: -10 + 10 = 0 10 + -56v + -9v2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -1.111111111 + 6.222222222v + v2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + 6.222222222v + 1.111111111 + v2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + 6.222222222v + v2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + 6.222222222v + v2 = 0 + 1.111111111 6.222222222v + v2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 6.222222222v + v2 = 1.111111111 The v term is 6.222222222v. Take half its coefficient (3.111111111). Square it (9.679012345) and add it to both sides. Add '9.679012345' to each side of the equation. 6.222222222v + 9.679012345 + v2 = 1.111111111 + 9.679012345 Reorder the terms: 9.679012345 + 6.222222222v + v2 = 1.111111111 + 9.679012345 Combine like terms: 1.111111111 + 9.679012345 = 10.790123456 9.679012345 + 6.222222222v + v2 = 10.790123456 Factor a perfect square on the left side: (v + 3.111111111)(v + 3.111111111) = 10.790123456 Calculate the square root of the right side: 3.284832333 Break this problem into two subproblems by setting (v + 3.111111111) equal to 3.284832333 and -3.284832333.Subproblem 1
v + 3.111111111 = 3.284832333 Simplifying v + 3.111111111 = 3.284832333 Reorder the terms: 3.111111111 + v = 3.284832333 Solving 3.111111111 + v = 3.284832333 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.111111111' to each side of the equation. 3.111111111 + -3.111111111 + v = 3.284832333 + -3.111111111 Combine like terms: 3.111111111 + -3.111111111 = 0.000000000 0.000000000 + v = 3.284832333 + -3.111111111 v = 3.284832333 + -3.111111111 Combine like terms: 3.284832333 + -3.111111111 = 0.173721222 v = 0.173721222 Simplifying v = 0.173721222Subproblem 2
v + 3.111111111 = -3.284832333 Simplifying v + 3.111111111 = -3.284832333 Reorder the terms: 3.111111111 + v = -3.284832333 Solving 3.111111111 + v = -3.284832333 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.111111111' to each side of the equation. 3.111111111 + -3.111111111 + v = -3.284832333 + -3.111111111 Combine like terms: 3.111111111 + -3.111111111 = 0.000000000 0.000000000 + v = -3.284832333 + -3.111111111 v = -3.284832333 + -3.111111111 Combine like terms: -3.284832333 + -3.111111111 = -6.395943444 v = -6.395943444 Simplifying v = -6.395943444Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.173721222, -6.395943444}
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