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Simplifying 2v2 + 24v + 73 = 2v + 49 Reorder the terms: 73 + 24v + 2v2 = 2v + 49 Reorder the terms: 73 + 24v + 2v2 = 49 + 2v Solving 73 + 24v + 2v2 = 49 + 2v Solving for variable 'v'. Reorder the terms: 73 + -49 + 24v + -2v + 2v2 = 49 + 2v + -49 + -2v Combine like terms: 73 + -49 = 24 24 + 24v + -2v + 2v2 = 49 + 2v + -49 + -2v Combine like terms: 24v + -2v = 22v 24 + 22v + 2v2 = 49 + 2v + -49 + -2v Reorder the terms: 24 + 22v + 2v2 = 49 + -49 + 2v + -2v Combine like terms: 49 + -49 = 0 24 + 22v + 2v2 = 0 + 2v + -2v 24 + 22v + 2v2 = 2v + -2v Combine like terms: 2v + -2v = 0 24 + 22v + 2v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 11v + v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + 11v + v2)' equal to zero and attempt to solve: Simplifying 12 + 11v + v2 = 0 Solving 12 + 11v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 11v + -12 + v2 = 0 + -12 Reorder the terms: 12 + -12 + 11v + v2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 11v + v2 = 0 + -12 11v + v2 = 0 + -12 Combine like terms: 0 + -12 = -12 11v + v2 = -12 The v term is 11v. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11v + 30.25 + v2 = -12 + 30.25 Reorder the terms: 30.25 + 11v + v2 = -12 + 30.25 Combine like terms: -12 + 30.25 = 18.25 30.25 + 11v + v2 = 18.25 Factor a perfect square on the left side: (v + 5.5)(v + 5.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (v + 5.5) equal to 4.272001873 and -4.272001873.Subproblem 1
v + 5.5 = 4.272001873 Simplifying v + 5.5 = 4.272001873 Reorder the terms: 5.5 + v = 4.272001873 Solving 5.5 + v = 4.272001873 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + v = 4.272001873 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + v = 4.272001873 + -5.5 v = 4.272001873 + -5.5 Combine like terms: 4.272001873 + -5.5 = -1.227998127 v = -1.227998127 Simplifying v = -1.227998127Subproblem 2
v + 5.5 = -4.272001873 Simplifying v + 5.5 = -4.272001873 Reorder the terms: 5.5 + v = -4.272001873 Solving 5.5 + v = -4.272001873 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + v = -4.272001873 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + v = -4.272001873 + -5.5 v = -4.272001873 + -5.5 Combine like terms: -4.272001873 + -5.5 = -9.772001873 v = -9.772001873 Simplifying v = -9.772001873Solution
The solution to the problem is based on the solutions from the subproblems. v = {-1.227998127, -9.772001873}Solution
v = {-1.227998127, -9.772001873}
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