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Simplifying 3v2 + -18v = 14 Reorder the terms: -18v + 3v2 = 14 Solving -18v + 3v2 = 14 Solving for variable 'v'. Reorder the terms: -14 + -18v + 3v2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -18v + 3v2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4.666666667 + -6v + v2 = 0 Move the constant term to the right: Add '4.666666667' to each side of the equation. -4.666666667 + -6v + 4.666666667 + v2 = 0 + 4.666666667 Reorder the terms: -4.666666667 + 4.666666667 + -6v + v2 = 0 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + -6v + v2 = 0 + 4.666666667 -6v + v2 = 0 + 4.666666667 Combine like terms: 0 + 4.666666667 = 4.666666667 -6v + v2 = 4.666666667 The v term is -6v. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6v + 9 + v2 = 4.666666667 + 9 Reorder the terms: 9 + -6v + v2 = 4.666666667 + 9 Combine like terms: 4.666666667 + 9 = 13.666666667 9 + -6v + v2 = 13.666666667 Factor a perfect square on the left side: (v + -3)(v + -3) = 13.666666667 Calculate the square root of the right side: 3.696845502 Break this problem into two subproblems by setting (v + -3) equal to 3.696845502 and -3.696845502.Subproblem 1
v + -3 = 3.696845502 Simplifying v + -3 = 3.696845502 Reorder the terms: -3 + v = 3.696845502 Solving -3 + v = 3.696845502 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = 3.696845502 + 3 Combine like terms: -3 + 3 = 0 0 + v = 3.696845502 + 3 v = 3.696845502 + 3 Combine like terms: 3.696845502 + 3 = 6.696845502 v = 6.696845502 Simplifying v = 6.696845502Subproblem 2
v + -3 = -3.696845502 Simplifying v + -3 = -3.696845502 Reorder the terms: -3 + v = -3.696845502 Solving -3 + v = -3.696845502 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = -3.696845502 + 3 Combine like terms: -3 + 3 = 0 0 + v = -3.696845502 + 3 v = -3.696845502 + 3 Combine like terms: -3.696845502 + 3 = -0.696845502 v = -0.696845502 Simplifying v = -0.696845502Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.696845502, -0.696845502}
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