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Simplifying -2v(v + -4) = -9v + -41 Reorder the terms: -2v(-4 + v) = -9v + -41 (-4 * -2v + v * -2v) = -9v + -41 (8v + -2v2) = -9v + -41 Reorder the terms: 8v + -2v2 = -41 + -9v Solving 8v + -2v2 = -41 + -9v Solving for variable 'v'. Reorder the terms: 41 + 8v + 9v + -2v2 = -41 + -9v + 41 + 9v Combine like terms: 8v + 9v = 17v 41 + 17v + -2v2 = -41 + -9v + 41 + 9v Reorder the terms: 41 + 17v + -2v2 = -41 + 41 + -9v + 9v Combine like terms: -41 + 41 = 0 41 + 17v + -2v2 = 0 + -9v + 9v 41 + 17v + -2v2 = -9v + 9v Combine like terms: -9v + 9v = 0 41 + 17v + -2v2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -20.5 + -8.5v + v2 = 0 Move the constant term to the right: Add '20.5' to each side of the equation. -20.5 + -8.5v + 20.5 + v2 = 0 + 20.5 Reorder the terms: -20.5 + 20.5 + -8.5v + v2 = 0 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + -8.5v + v2 = 0 + 20.5 -8.5v + v2 = 0 + 20.5 Combine like terms: 0 + 20.5 = 20.5 -8.5v + v2 = 20.5 The v term is -8.5v. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5v + 18.0625 + v2 = 20.5 + 18.0625 Reorder the terms: 18.0625 + -8.5v + v2 = 20.5 + 18.0625 Combine like terms: 20.5 + 18.0625 = 38.5625 18.0625 + -8.5v + v2 = 38.5625 Factor a perfect square on the left side: (v + -4.25)(v + -4.25) = 38.5625 Calculate the square root of the right side: 6.209871174 Break this problem into two subproblems by setting (v + -4.25) equal to 6.209871174 and -6.209871174.Subproblem 1
v + -4.25 = 6.209871174 Simplifying v + -4.25 = 6.209871174 Reorder the terms: -4.25 + v = 6.209871174 Solving -4.25 + v = 6.209871174 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + v = 6.209871174 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + v = 6.209871174 + 4.25 v = 6.209871174 + 4.25 Combine like terms: 6.209871174 + 4.25 = 10.459871174 v = 10.459871174 Simplifying v = 10.459871174Subproblem 2
v + -4.25 = -6.209871174 Simplifying v + -4.25 = -6.209871174 Reorder the terms: -4.25 + v = -6.209871174 Solving -4.25 + v = -6.209871174 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + v = -6.209871174 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + v = -6.209871174 + 4.25 v = -6.209871174 + 4.25 Combine like terms: -6.209871174 + 4.25 = -1.959871174 v = -1.959871174 Simplifying v = -1.959871174Solution
The solution to the problem is based on the solutions from the subproblems. v = {10.459871174, -1.959871174}
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