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Simplifying v2 + 2v + -54 = 0 Reorder the terms: -54 + 2v + v2 = 0 Solving -54 + 2v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + 2v + 54 + v2 = 0 + 54 Reorder the terms: -54 + 54 + 2v + v2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 2v + v2 = 0 + 54 2v + v2 = 0 + 54 Combine like terms: 0 + 54 = 54 2v + v2 = 54 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 = 54 + 1 Reorder the terms: 1 + 2v + v2 = 54 + 1 Combine like terms: 54 + 1 = 55 1 + 2v + v2 = 55 Factor a perfect square on the left side: (v + 1)(v + 1) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (v + 1) equal to 7.416198487 and -7.416198487.Subproblem 1
v + 1 = 7.416198487 Simplifying v + 1 = 7.416198487 Reorder the terms: 1 + v = 7.416198487 Solving 1 + v = 7.416198487 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 = 7.416198487 + -1 Combine like terms: 1 + -1 = 0 0 + v = 7.416198487 + -1 v = 7.416198487 + -1 Combine like terms: 7.416198487 + -1 = 6.416198487 v = 6.416198487 Simplifying v = 6.416198487Subproblem 2
v + 1 = -7.416198487 Simplifying v + 1 = -7.416198487 Reorder the terms: 1 + v = -7.416198487 Solving 1 + v = -7.416198487 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 = -7.416198487 + -1 Combine like terms: 1 + -1 = 0 0 + v = -7.416198487 + -1 v = -7.416198487 + -1 Combine like terms: -7.416198487 + -1 = -8.416198487 v = -8.416198487 Simplifying v = -8.416198487Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.416198487, -8.416198487}
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