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Simplifying 2v2 + 9v + 43 = v2 + 49 Reorder the terms: 43 + 9v + 2v2 = v2 + 49 Reorder the terms: 43 + 9v + 2v2 = 49 + v2 Solving 43 + 9v + 2v2 = 49 + v2 Solving for variable 'v'. Reorder the terms: 43 + -49 + 9v + 2v2 + -1v2 = 49 + v2 + -49 + -1v2 Combine like terms: 43 + -49 = -6 -6 + 9v + 2v2 + -1v2 = 49 + v2 + -49 + -1v2 Combine like terms: 2v2 + -1v2 = 1v2 -6 + 9v + 1v2 = 49 + v2 + -49 + -1v2 Reorder the terms: -6 + 9v + 1v2 = 49 + -49 + v2 + -1v2 Combine like terms: 49 + -49 = 0 -6 + 9v + 1v2 = 0 + v2 + -1v2 -6 + 9v + 1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 -6 + 9v + 1v2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 9v + 6 + v2 = 0 + 6 Reorder the terms: -6 + 6 + 9v + v2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 9v + v2 = 0 + 6 9v + v2 = 0 + 6 Combine like terms: 0 + 6 = 6 9v + v2 = 6 The v term is 9v. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9v + 20.25 + v2 = 6 + 20.25 Reorder the terms: 20.25 + 9v + v2 = 6 + 20.25 Combine like terms: 6 + 20.25 = 26.25 20.25 + 9v + v2 = 26.25 Factor a perfect square on the left side: (v + 4.5)(v + 4.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (v + 4.5) equal to 5.123475383 and -5.123475383.Subproblem 1
v + 4.5 = 5.123475383 Simplifying v + 4.5 = 5.123475383 Reorder the terms: 4.5 + v = 5.123475383 Solving 4.5 + v = 5.123475383 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + v = 5.123475383 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + v = 5.123475383 + -4.5 v = 5.123475383 + -4.5 Combine like terms: 5.123475383 + -4.5 = 0.623475383 v = 0.623475383 Simplifying v = 0.623475383Subproblem 2
v + 4.5 = -5.123475383 Simplifying v + 4.5 = -5.123475383 Reorder the terms: 4.5 + v = -5.123475383 Solving 4.5 + v = -5.123475383 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + v = -5.123475383 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + v = -5.123475383 + -4.5 v = -5.123475383 + -4.5 Combine like terms: -5.123475383 + -4.5 = -9.623475383 v = -9.623475383 Simplifying v = -9.623475383Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.623475383, -9.623475383}
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