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Simplifying v2 + 2v + -24 = 9 Reorder the terms: -24 + 2v + v2 = 9 Solving -24 + 2v + v2 = 9 Solving for variable 'v'. Reorder the terms: -24 + -9 + 2v + v2 = 9 + -9 Combine like terms: -24 + -9 = -33 -33 + 2v + v2 = 9 + -9 Combine like terms: 9 + -9 = 0 -33 + 2v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + 2v + 33 + v2 = 0 + 33 Reorder the terms: -33 + 33 + 2v + v2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 2v + v2 = 0 + 33 2v + v2 = 0 + 33 Combine like terms: 0 + 33 = 33 2v + v2 = 33 The v term is 2v. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2v + 1 + v2 = 33 + 1 Reorder the terms: 1 + 2v + v2 = 33 + 1 Combine like terms: 33 + 1 = 34 1 + 2v + v2 = 34 Factor a perfect square on the left side: (v + 1)(v + 1) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (v + 1) equal to 5.830951895 and -5.830951895.Subproblem 1
v + 1 = 5.830951895 Simplifying v + 1 = 5.830951895 Reorder the terms: 1 + v = 5.830951895 Solving 1 + v = 5.830951895 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = 5.830951895 + -1 Combine like terms: 1 + -1 = 0 0 + v = 5.830951895 + -1 v = 5.830951895 + -1 Combine like terms: 5.830951895 + -1 = 4.830951895 v = 4.830951895 Simplifying v = 4.830951895Subproblem 2
v + 1 = -5.830951895 Simplifying v + 1 = -5.830951895 Reorder the terms: 1 + v = -5.830951895 Solving 1 + v = -5.830951895 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = -5.830951895 + -1 Combine like terms: 1 + -1 = 0 0 + v = -5.830951895 + -1 v = -5.830951895 + -1 Combine like terms: -5.830951895 + -1 = -6.830951895 v = -6.830951895 Simplifying v = -6.830951895Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.830951895, -6.830951895}
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