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Simplifying v2 = -2v + 4 Reorder the terms: v2 = 4 + -2v Solving v2 = 4 + -2v Solving for variable 'v'. Reorder the terms: -4 + 2v + v2 = 4 + -2v + -4 + 2v Reorder the terms: -4 + 2v + v2 = 4 + -4 + -2v + 2v Combine like terms: 4 + -4 = 0 -4 + 2v + v2 = 0 + -2v + 2v -4 + 2v + v2 = -2v + 2v Combine like terms: -2v + 2v = 0 -4 + 2v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 2v + 4 + v2 = 0 + 4 Reorder the terms: -4 + 4 + 2v + v2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2v + v2 = 0 + 4 2v + v2 = 0 + 4 Combine like terms: 0 + 4 = 4 2v + v2 = 4 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 = 4 + 1 Reorder the terms: 1 + 2v + v2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + 2v + v2 = 5 Factor a perfect square on the left side: (v + 1)(v + 1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (v + 1) equal to 2.236067978 and -2.236067978.Subproblem 1
v + 1 = 2.236067978 Simplifying v + 1 = 2.236067978 Reorder the terms: 1 + v = 2.236067978 Solving 1 + v = 2.236067978 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 = 2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + v = 2.236067978 + -1 v = 2.236067978 + -1 Combine like terms: 2.236067978 + -1 = 1.236067978 v = 1.236067978 Simplifying v = 1.236067978Subproblem 2
v + 1 = -2.236067978 Simplifying v + 1 = -2.236067978 Reorder the terms: 1 + v = -2.236067978 Solving 1 + v = -2.236067978 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 = -2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + v = -2.236067978 + -1 v = -2.236067978 + -1 Combine like terms: -2.236067978 + -1 = -3.236067978 v = -3.236067978 Simplifying v = -3.236067978Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.236067978, -3.236067978}
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