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Simplifying 6v2 + -21v + 10 = 0 Reorder the terms: 10 + -21v + 6v2 = 0 Solving 10 + -21v + 6v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.666666667 + -3.5v + v2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -3.5v + -1.666666667 + v2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -3.5v + v2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -3.5v + v2 = 0 + -1.666666667 -3.5v + v2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -3.5v + v2 = -1.666666667 The v term is -3.5v. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5v + 3.0625 + v2 = -1.666666667 + 3.0625 Reorder the terms: 3.0625 + -3.5v + v2 = -1.666666667 + 3.0625 Combine like terms: -1.666666667 + 3.0625 = 1.395833333 3.0625 + -3.5v + v2 = 1.395833333 Factor a perfect square on the left side: (v + -1.75)(v + -1.75) = 1.395833333 Calculate the square root of the right side: 1.181453906 Break this problem into two subproblems by setting (v + -1.75) equal to 1.181453906 and -1.181453906.Subproblem 1
v + -1.75 = 1.181453906 Simplifying v + -1.75 = 1.181453906 Reorder the terms: -1.75 + v = 1.181453906 Solving -1.75 + v = 1.181453906 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + v = 1.181453906 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + v = 1.181453906 + 1.75 v = 1.181453906 + 1.75 Combine like terms: 1.181453906 + 1.75 = 2.931453906 v = 2.931453906 Simplifying v = 2.931453906Subproblem 2
v + -1.75 = -1.181453906 Simplifying v + -1.75 = -1.181453906 Reorder the terms: -1.75 + v = -1.181453906 Solving -1.75 + v = -1.181453906 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + v = -1.181453906 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + v = -1.181453906 + 1.75 v = -1.181453906 + 1.75 Combine like terms: -1.181453906 + 1.75 = 0.568546094 v = 0.568546094 Simplifying v = 0.568546094Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.931453906, 0.568546094}
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