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Simplifying 3v2 + -27v + 55 = 0 Reorder the terms: 55 + -27v + 3v2 = 0 Solving 55 + -27v + 3v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 18.33333333 + -9v + v2 = 0 Move the constant term to the right: Add '-18.33333333' to each side of the equation. 18.33333333 + -9v + -18.33333333 + v2 = 0 + -18.33333333 Reorder the terms: 18.33333333 + -18.33333333 + -9v + v2 = 0 + -18.33333333 Combine like terms: 18.33333333 + -18.33333333 = 0.00000000 0.00000000 + -9v + v2 = 0 + -18.33333333 -9v + v2 = 0 + -18.33333333 Combine like terms: 0 + -18.33333333 = -18.33333333 -9v + v2 = -18.33333333 The v term is -9v. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9v + 20.25 + v2 = -18.33333333 + 20.25 Reorder the terms: 20.25 + -9v + v2 = -18.33333333 + 20.25 Combine like terms: -18.33333333 + 20.25 = 1.91666667 20.25 + -9v + v2 = 1.91666667 Factor a perfect square on the left side: (v + -4.5)(v + -4.5) = 1.91666667 Calculate the square root of the right side: 1.384437312 Break this problem into two subproblems by setting (v + -4.5) equal to 1.384437312 and -1.384437312.Subproblem 1
v + -4.5 = 1.384437312 Simplifying v + -4.5 = 1.384437312 Reorder the terms: -4.5 + v = 1.384437312 Solving -4.5 + v = 1.384437312 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + v = 1.384437312 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + v = 1.384437312 + 4.5 v = 1.384437312 + 4.5 Combine like terms: 1.384437312 + 4.5 = 5.884437312 v = 5.884437312 Simplifying v = 5.884437312Subproblem 2
v + -4.5 = -1.384437312 Simplifying v + -4.5 = -1.384437312 Reorder the terms: -4.5 + v = -1.384437312 Solving -4.5 + v = -1.384437312 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + v = -1.384437312 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + v = -1.384437312 + 4.5 v = -1.384437312 + 4.5 Combine like terms: -1.384437312 + 4.5 = 3.115562688 v = 3.115562688 Simplifying v = 3.115562688Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.884437312, 3.115562688}
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