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Simplifying 5v2 + -20 = 10v Reorder the terms: -20 + 5v2 = 10v Solving -20 + 5v2 = 10v Solving for variable 'v'. Reorder the terms: -20 + -10v + 5v2 = 10v + -10v Combine like terms: 10v + -10v = 0 -20 + -10v + 5v2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-4 + -2v + v2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-4 + -2v + v2)' equal to zero and attempt to solve: Simplifying -4 + -2v + v2 = 0 Solving -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 = 3.236067978 v = 3.236067978 Simplifying v = 3.236067978Subproblem 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 = -1.236067978 v = -1.236067978 Simplifying v = -1.236067978Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.236067978, -1.236067978}Solution
v = {3.236067978, -1.236067978}
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