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Simplifying v2 + 17v + 24 = 0 Reorder the terms: 24 + 17v + v2 = 0 Solving 24 + 17v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 17v + -24 + v2 = 0 + -24 Reorder the terms: 24 + -24 + 17v + v2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 17v + v2 = 0 + -24 17v + v2 = 0 + -24 Combine like terms: 0 + -24 = -24 17v + v2 = -24 The v term is 17v. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17v + 72.25 + v2 = -24 + 72.25 Reorder the terms: 72.25 + 17v + v2 = -24 + 72.25 Combine like terms: -24 + 72.25 = 48.25 72.25 + 17v + v2 = 48.25 Factor a perfect square on the left side: (v + 8.5)(v + 8.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (v + 8.5) equal to 6.946221995 and -6.946221995.Subproblem 1
v + 8.5 = 6.946221995 Simplifying v + 8.5 = 6.946221995 Reorder the terms: 8.5 + v = 6.946221995 Solving 8.5 + v = 6.946221995 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + v = 6.946221995 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + v = 6.946221995 + -8.5 v = 6.946221995 + -8.5 Combine like terms: 6.946221995 + -8.5 = -1.553778005 v = -1.553778005 Simplifying v = -1.553778005Subproblem 2
v + 8.5 = -6.946221995 Simplifying v + 8.5 = -6.946221995 Reorder the terms: 8.5 + v = -6.946221995 Solving 8.5 + v = -6.946221995 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + v = -6.946221995 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + v = -6.946221995 + -8.5 v = -6.946221995 + -8.5 Combine like terms: -6.946221995 + -8.5 = -15.446221995 v = -15.446221995 Simplifying v = -15.446221995Solution
The solution to the problem is based on the solutions from the subproblems. v = {-1.553778005, -15.446221995}
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