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Simplifying v(8v + -25) = -9 Reorder the terms: v(-25 + 8v) = -9 (-25 * v + 8v * v) = -9 (-25v + 8v2) = -9 Solving -25v + 8v2 = -9 Solving for variable 'v'. Reorder the terms: 9 + -25v + 8v2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -25v + 8v2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + -3.125v + v2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -3.125v + -1.125 + v2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -3.125v + v2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -3.125v + v2 = 0 + -1.125 -3.125v + v2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -3.125v + v2 = -1.125 The v term is -3.125v. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125v + 2.44140625 + v2 = -1.125 + 2.44140625 Reorder the terms: 2.44140625 + -3.125v + v2 = -1.125 + 2.44140625 Combine like terms: -1.125 + 2.44140625 = 1.31640625 2.44140625 + -3.125v + v2 = 1.31640625 Factor a perfect square on the left side: (v + -1.5625)(v + -1.5625) = 1.31640625 Calculate the square root of the right side: 1.147347484 Break this problem into two subproblems by setting (v + -1.5625) equal to 1.147347484 and -1.147347484.Subproblem 1
v + -1.5625 = 1.147347484 Simplifying v + -1.5625 = 1.147347484 Reorder the terms: -1.5625 + v = 1.147347484 Solving -1.5625 + v = 1.147347484 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + v = 1.147347484 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + v = 1.147347484 + 1.5625 v = 1.147347484 + 1.5625 Combine like terms: 1.147347484 + 1.5625 = 2.709847484 v = 2.709847484 Simplifying v = 2.709847484Subproblem 2
v + -1.5625 = -1.147347484 Simplifying v + -1.5625 = -1.147347484 Reorder the terms: -1.5625 + v = -1.147347484 Solving -1.5625 + v = -1.147347484 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + v = -1.147347484 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + v = -1.147347484 + 1.5625 v = -1.147347484 + 1.5625 Combine like terms: -1.147347484 + 1.5625 = 0.415152516 v = 0.415152516 Simplifying v = 0.415152516Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.709847484, 0.415152516}
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