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Simplifying v2 + 6v + -24 = -18 Reorder the terms: -24 + 6v + v2 = -18 Solving -24 + 6v + v2 = -18 Solving for variable 'v'. Reorder the terms: -24 + 18 + 6v + v2 = -18 + 18 Combine like terms: -24 + 18 = -6 -6 + 6v + v2 = -18 + 18 Combine like terms: -18 + 18 = 0 -6 + 6v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 6v + 6 + v2 = 0 + 6 Reorder the terms: -6 + 6 + 6v + v2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 6v + v2 = 0 + 6 6v + v2 = 0 + 6 Combine like terms: 0 + 6 = 6 6v + v2 = 6 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 = 6 + 9 Reorder the terms: 9 + 6v + v2 = 6 + 9 Combine like terms: 6 + 9 = 15 9 + 6v + v2 = 15 Factor a perfect square on the left side: (v + 3)(v + 3) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (v + 3) equal to 3.872983346 and -3.872983346.Subproblem 1
v + 3 = 3.872983346 Simplifying v + 3 = 3.872983346 Reorder the terms: 3 + v = 3.872983346 Solving 3 + v = 3.872983346 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 = 3.872983346 + -3 Combine like terms: 3 + -3 = 0 0 + v = 3.872983346 + -3 v = 3.872983346 + -3 Combine like terms: 3.872983346 + -3 = 0.872983346 v = 0.872983346 Simplifying v = 0.872983346Subproblem 2
v + 3 = -3.872983346 Simplifying v + 3 = -3.872983346 Reorder the terms: 3 + v = -3.872983346 Solving 3 + v = -3.872983346 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 = -3.872983346 + -3 Combine like terms: 3 + -3 = 0 0 + v = -3.872983346 + -3 v = -3.872983346 + -3 Combine like terms: -3.872983346 + -3 = -6.872983346 v = -6.872983346 Simplifying v = -6.872983346Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.872983346, -6.872983346}
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