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Simplifying v2 + -6v + -9 = 0 Reorder the terms: -9 + -6v + v2 = 0 Solving -9 + -6v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -6v + 9 + v2 = 0 + 9 Reorder the terms: -9 + 9 + -6v + v2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -6v + v2 = 0 + 9 -6v + v2 = 0 + 9 Combine like terms: 0 + 9 = 9 -6v + v2 = 9 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 = 9 + 9 Reorder the terms: 9 + -6v + v2 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + -6v + v2 = 18 Factor a perfect square on the left side: (v + -3)(v + -3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (v + -3) equal to 4.242640687 and -4.242640687.Subproblem 1
v + -3 = 4.242640687 Simplifying v + -3 = 4.242640687 Reorder the terms: -3 + v = 4.242640687 Solving -3 + v = 4.242640687 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 = 4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + v = 4.242640687 + 3 v = 4.242640687 + 3 Combine like terms: 4.242640687 + 3 = 7.242640687 v = 7.242640687 Simplifying v = 7.242640687Subproblem 2
v + -3 = -4.242640687 Simplifying v + -3 = -4.242640687 Reorder the terms: -3 + v = -4.242640687 Solving -3 + v = -4.242640687 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 = -4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + v = -4.242640687 + 3 v = -4.242640687 + 3 Combine like terms: -4.242640687 + 3 = -1.242640687 v = -1.242640687 Simplifying v = -1.242640687Solution
The solution to the problem is based on the solutions from the subproblems. v = {7.242640687, -1.242640687}
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