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Simplifying 3v2 + -27v + 56 = 0 Reorder the terms: 56 + -27v + 3v2 = 0 Solving 56 + -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'. 18.66666667 + -9v + v2 = 0 Move the constant term to the right: Add '-18.66666667' to each side of the equation. 18.66666667 + -9v + -18.66666667 + v2 = 0 + -18.66666667 Reorder the terms: 18.66666667 + -18.66666667 + -9v + v2 = 0 + -18.66666667 Combine like terms: 18.66666667 + -18.66666667 = 0.00000000 0.00000000 + -9v + v2 = 0 + -18.66666667 -9v + v2 = 0 + -18.66666667 Combine like terms: 0 + -18.66666667 = -18.66666667 -9v + v2 = -18.66666667 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 = -18.66666667 + 20.25 Reorder the terms: 20.25 + -9v + v2 = -18.66666667 + 20.25 Combine like terms: -18.66666667 + 20.25 = 1.58333333 20.25 + -9v + v2 = 1.58333333 Factor a perfect square on the left side: (v + -4.5)(v + -4.5) = 1.58333333 Calculate the square root of the right side: 1.258305738 Break this problem into two subproblems by setting (v + -4.5) equal to 1.258305738 and -1.258305738.Subproblem 1
v + -4.5 = 1.258305738 Simplifying v + -4.5 = 1.258305738 Reorder the terms: -4.5 + v = 1.258305738 Solving -4.5 + v = 1.258305738 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 = 1.258305738 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + v = 1.258305738 + 4.5 v = 1.258305738 + 4.5 Combine like terms: 1.258305738 + 4.5 = 5.758305738 v = 5.758305738 Simplifying v = 5.758305738Subproblem 2
v + -4.5 = -1.258305738 Simplifying v + -4.5 = -1.258305738 Reorder the terms: -4.5 + v = -1.258305738 Solving -4.5 + v = -1.258305738 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 = -1.258305738 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + v = -1.258305738 + 4.5 v = -1.258305738 + 4.5 Combine like terms: -1.258305738 + 4.5 = 3.241694262 v = 3.241694262 Simplifying v = 3.241694262Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.758305738, 3.241694262}
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