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Simplifying 21v + -8v2 + -9 = 0 Reorder the terms: -9 + 21v + -8v2 = 0 Solving -9 + 21v + -8v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 1.125 + -2.625v + v2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -2.625v + -1.125 + v2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -2.625v + v2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -2.625v + v2 = 0 + -1.125 -2.625v + v2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -2.625v + v2 = -1.125 The v term is -2.625v. Take half its coefficient (-1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. -2.625v + 1.72265625 + v2 = -1.125 + 1.72265625 Reorder the terms: 1.72265625 + -2.625v + v2 = -1.125 + 1.72265625 Combine like terms: -1.125 + 1.72265625 = 0.59765625 1.72265625 + -2.625v + v2 = 0.59765625 Factor a perfect square on the left side: (v + -1.3125)(v + -1.3125) = 0.59765625 Calculate the square root of the right side: 0.773082305 Break this problem into two subproblems by setting (v + -1.3125) equal to 0.773082305 and -0.773082305.Subproblem 1
v + -1.3125 = 0.773082305 Simplifying v + -1.3125 = 0.773082305 Reorder the terms: -1.3125 + v = 0.773082305 Solving -1.3125 + v = 0.773082305 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + v = 0.773082305 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + v = 0.773082305 + 1.3125 v = 0.773082305 + 1.3125 Combine like terms: 0.773082305 + 1.3125 = 2.085582305 v = 2.085582305 Simplifying v = 2.085582305Subproblem 2
v + -1.3125 = -0.773082305 Simplifying v + -1.3125 = -0.773082305 Reorder the terms: -1.3125 + v = -0.773082305 Solving -1.3125 + v = -0.773082305 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + v = -0.773082305 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + v = -0.773082305 + 1.3125 v = -0.773082305 + 1.3125 Combine like terms: -0.773082305 + 1.3125 = 0.539417695 v = 0.539417695 Simplifying v = 0.539417695Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.085582305, 0.539417695}
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