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Simplifying v2 + 7v + -24 = -8 Reorder the terms: -24 + 7v + v2 = -8 Solving -24 + 7v + v2 = -8 Solving for variable 'v'. Reorder the terms: -24 + 8 + 7v + v2 = -8 + 8 Combine like terms: -24 + 8 = -16 -16 + 7v + v2 = -8 + 8 Combine like terms: -8 + 8 = 0 -16 + 7v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 7v + 16 + v2 = 0 + 16 Reorder the terms: -16 + 16 + 7v + v2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 7v + v2 = 0 + 16 7v + v2 = 0 + 16 Combine like terms: 0 + 16 = 16 7v + v2 = 16 The v term is 7v. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7v + 12.25 + v2 = 16 + 12.25 Reorder the terms: 12.25 + 7v + v2 = 16 + 12.25 Combine like terms: 16 + 12.25 = 28.25 12.25 + 7v + v2 = 28.25 Factor a perfect square on the left side: (v + 3.5)(v + 3.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (v + 3.5) equal to 5.315072906 and -5.315072906.Subproblem 1
v + 3.5 = 5.315072906 Simplifying v + 3.5 = 5.315072906 Reorder the terms: 3.5 + v = 5.315072906 Solving 3.5 + v = 5.315072906 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + v = 5.315072906 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + v = 5.315072906 + -3.5 v = 5.315072906 + -3.5 Combine like terms: 5.315072906 + -3.5 = 1.815072906 v = 1.815072906 Simplifying v = 1.815072906Subproblem 2
v + 3.5 = -5.315072906 Simplifying v + 3.5 = -5.315072906 Reorder the terms: 3.5 + v = -5.315072906 Solving 3.5 + v = -5.315072906 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + v = -5.315072906 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + v = -5.315072906 + -3.5 v = -5.315072906 + -3.5 Combine like terms: -5.315072906 + -3.5 = -8.815072906 v = -8.815072906 Simplifying v = -8.815072906Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.815072906, -8.815072906}
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