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Simplifying v2 + -2v + -57 = -4 Reorder the terms: -57 + -2v + v2 = -4 Solving -57 + -2v + v2 = -4 Solving for variable 'v'. Reorder the terms: -57 + 4 + -2v + v2 = -4 + 4 Combine like terms: -57 + 4 = -53 -53 + -2v + v2 = -4 + 4 Combine like terms: -4 + 4 = 0 -53 + -2v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + -2v + 53 + v2 = 0 + 53 Reorder the terms: -53 + 53 + -2v + v2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + -2v + v2 = 0 + 53 -2v + v2 = 0 + 53 Combine like terms: 0 + 53 = 53 -2v + v2 = 53 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 = 53 + 1 Reorder the terms: 1 + -2v + v2 = 53 + 1 Combine like terms: 53 + 1 = 54 1 + -2v + v2 = 54 Factor a perfect square on the left side: (v + -1)(v + -1) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (v + -1) equal to 7.348469228 and -7.348469228.Subproblem 1
v + -1 = 7.348469228 Simplifying v + -1 = 7.348469228 Reorder the terms: -1 + v = 7.348469228 Solving -1 + v = 7.348469228 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 = 7.348469228 + 1 Combine like terms: -1 + 1 = 0 0 + v = 7.348469228 + 1 v = 7.348469228 + 1 Combine like terms: 7.348469228 + 1 = 8.348469228 v = 8.348469228 Simplifying v = 8.348469228Subproblem 2
v + -1 = -7.348469228 Simplifying v + -1 = -7.348469228 Reorder the terms: -1 + v = -7.348469228 Solving -1 + v = -7.348469228 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 = -7.348469228 + 1 Combine like terms: -1 + 1 = 0 0 + v = -7.348469228 + 1 v = -7.348469228 + 1 Combine like terms: -7.348469228 + 1 = -6.348469228 v = -6.348469228 Simplifying v = -6.348469228Solution
The solution to the problem is based on the solutions from the subproblems. v = {8.348469228, -6.348469228}
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