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Simplifying (v + 5)(v + -3) = 1 Reorder the terms: (5 + v)(v + -3) = 1 Reorder the terms: (5 + v)(-3 + v) = 1 Multiply (5 + v) * (-3 + v) (5(-3 + v) + v(-3 + v)) = 1 ((-3 * 5 + v * 5) + v(-3 + v)) = 1 ((-15 + 5v) + v(-3 + v)) = 1 (-15 + 5v + (-3 * v + v * v)) = 1 (-15 + 5v + (-3v + v2)) = 1 Combine like terms: 5v + -3v = 2v (-15 + 2v + v2) = 1 Solving -15 + 2v + v2 = 1 Solving for variable 'v'. Reorder the terms: -15 + -1 + 2v + v2 = 1 + -1 Combine like terms: -15 + -1 = -16 -16 + 2v + v2 = 1 + -1 Combine like terms: 1 + -1 = 0 -16 + 2v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 2v + 16 + v2 = 0 + 16 Reorder the terms: -16 + 16 + 2v + v2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 2v + v2 = 0 + 16 2v + v2 = 0 + 16 Combine like terms: 0 + 16 = 16 2v + v2 = 16 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 = 16 + 1 Reorder the terms: 1 + 2v + v2 = 16 + 1 Combine like terms: 16 + 1 = 17 1 + 2v + v2 = 17 Factor a perfect square on the left side: (v + 1)(v + 1) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (v + 1) equal to 4.123105626 and -4.123105626.Subproblem 1
v + 1 = 4.123105626 Simplifying v + 1 = 4.123105626 Reorder the terms: 1 + v = 4.123105626 Solving 1 + v = 4.123105626 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 = 4.123105626 + -1 Combine like terms: 1 + -1 = 0 0 + v = 4.123105626 + -1 v = 4.123105626 + -1 Combine like terms: 4.123105626 + -1 = 3.123105626 v = 3.123105626 Simplifying v = 3.123105626Subproblem 2
v + 1 = -4.123105626 Simplifying v + 1 = -4.123105626 Reorder the terms: 1 + v = -4.123105626 Solving 1 + v = -4.123105626 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 = -4.123105626 + -1 Combine like terms: 1 + -1 = 0 0 + v = -4.123105626 + -1 v = -4.123105626 + -1 Combine like terms: -4.123105626 + -1 = -5.123105626 v = -5.123105626 Simplifying v = -5.123105626Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.123105626, -5.123105626}
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