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Simplifying 2n2 + -4n = 8 Reorder the terms: -4n + 2n2 = 8 Solving -4n + 2n2 = 8 Solving for variable 'n'. Reorder the terms: -8 + -4n + 2n2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -4n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -2n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -2n + n2)' equal to zero and attempt to solve: Simplifying -4 + -2n + n2 = 0 Solving -4 + -2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -2n + 4 + n2 = 0 + 4 Reorder the terms: -4 + 4 + -2n + n2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2n + n2 = 0 + 4 -2n + n2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2n + n2 = 4 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = 4 + 1 Reorder the terms: 1 + -2n + n2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + -2n + n2 = 5 Factor a perfect square on the left side: (n + -1)(n + -1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (n + -1) equal to 2.236067978 and -2.236067978.Subproblem 1
n + -1 = 2.236067978 Simplifying n + -1 = 2.236067978 Reorder the terms: -1 + n = 2.236067978 Solving -1 + n = 2.236067978 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + n = 2.236067978 + 1 n = 2.236067978 + 1 Combine like terms: 2.236067978 + 1 = 3.236067978 n = 3.236067978 Simplifying n = 3.236067978Subproblem 2
n + -1 = -2.236067978 Simplifying n + -1 = -2.236067978 Reorder the terms: -1 + n = -2.236067978 Solving -1 + n = -2.236067978 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + n = -2.236067978 + 1 n = -2.236067978 + 1 Combine like terms: -2.236067978 + 1 = -1.236067978 n = -1.236067978 Simplifying n = -1.236067978Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.236067978, -1.236067978}Solution
n = {3.236067978, -1.236067978}
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