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Simplifying v2 + 15v + 44 = v Reorder the terms: 44 + 15v + v2 = v Solving 44 + 15v + v2 = v Solving for variable 'v'. Reorder the terms: 44 + 15v + -1v + v2 = v + -1v Combine like terms: 15v + -1v = 14v 44 + 14v + v2 = v + -1v Combine like terms: v + -1v = 0 44 + 14v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-44' to each side of the equation. 44 + 14v + -44 + v2 = 0 + -44 Reorder the terms: 44 + -44 + 14v + v2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + 14v + v2 = 0 + -44 14v + v2 = 0 + -44 Combine like terms: 0 + -44 = -44 14v + v2 = -44 The v term is 14v. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14v + 49 + v2 = -44 + 49 Reorder the terms: 49 + 14v + v2 = -44 + 49 Combine like terms: -44 + 49 = 5 49 + 14v + v2 = 5 Factor a perfect square on the left side: (v + 7)(v + 7) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (v + 7) equal to 2.236067978 and -2.236067978.Subproblem 1
v + 7 = 2.236067978 Simplifying v + 7 = 2.236067978 Reorder the terms: 7 + v = 2.236067978 Solving 7 + v = 2.236067978 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + v = 2.236067978 + -7 Combine like terms: 7 + -7 = 0 0 + v = 2.236067978 + -7 v = 2.236067978 + -7 Combine like terms: 2.236067978 + -7 = -4.763932022 v = -4.763932022 Simplifying v = -4.763932022Subproblem 2
v + 7 = -2.236067978 Simplifying v + 7 = -2.236067978 Reorder the terms: 7 + v = -2.236067978 Solving 7 + v = -2.236067978 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + v = -2.236067978 + -7 Combine like terms: 7 + -7 = 0 0 + v = -2.236067978 + -7 v = -2.236067978 + -7 Combine like terms: -2.236067978 + -7 = -9.236067978 v = -9.236067978 Simplifying v = -9.236067978Solution
The solution to the problem is based on the solutions from the subproblems. v = {-4.763932022, -9.236067978}
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