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Simplifying n2 + 4n + -89 = 0 Reorder the terms: -89 + 4n + n2 = 0 Solving -89 + 4n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '89' to each side of the equation. -89 + 4n + 89 + n2 = 0 + 89 Reorder the terms: -89 + 89 + 4n + n2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + 4n + n2 = 0 + 89 4n + n2 = 0 + 89 Combine like terms: 0 + 89 = 89 4n + n2 = 89 The n term is 4n. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4n + 4 + n2 = 89 + 4 Reorder the terms: 4 + 4n + n2 = 89 + 4 Combine like terms: 89 + 4 = 93 4 + 4n + n2 = 93 Factor a perfect square on the left side: (n + 2)(n + 2) = 93 Calculate the square root of the right side: 9.643650761 Break this problem into two subproblems by setting (n + 2) equal to 9.643650761 and -9.643650761.Subproblem 1
n + 2 = 9.643650761 Simplifying n + 2 = 9.643650761 Reorder the terms: 2 + n = 9.643650761 Solving 2 + n = 9.643650761 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 9.643650761 + -2 Combine like terms: 2 + -2 = 0 0 + n = 9.643650761 + -2 n = 9.643650761 + -2 Combine like terms: 9.643650761 + -2 = 7.643650761 n = 7.643650761 Simplifying n = 7.643650761Subproblem 2
n + 2 = -9.643650761 Simplifying n + 2 = -9.643650761 Reorder the terms: 2 + n = -9.643650761 Solving 2 + n = -9.643650761 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = -9.643650761 + -2 Combine like terms: 2 + -2 = 0 0 + n = -9.643650761 + -2 n = -9.643650761 + -2 Combine like terms: -9.643650761 + -2 = -11.643650761 n = -11.643650761 Simplifying n = -11.643650761Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.643650761, -11.643650761}
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