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Simplifying n2 + 3n + -18 = n Reorder the terms: -18 + 3n + n2 = n Solving -18 + 3n + n2 = n Solving for variable 'n'. Reorder the terms: -18 + 3n + -1n + n2 = n + -1n Combine like terms: 3n + -1n = 2n -18 + 2n + n2 = n + -1n Combine like terms: n + -1n = 0 -18 + 2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 2n + 18 + n2 = 0 + 18 Reorder the terms: -18 + 18 + 2n + n2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 2n + n2 = 0 + 18 2n + n2 = 0 + 18 Combine like terms: 0 + 18 = 18 2n + n2 = 18 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 = 18 + 1 Reorder the terms: 1 + 2n + n2 = 18 + 1 Combine like terms: 18 + 1 = 19 1 + 2n + n2 = 19 Factor a perfect square on the left side: (n + 1)(n + 1) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (n + 1) equal to 4.358898944 and -4.358898944.Subproblem 1
n + 1 = 4.358898944 Simplifying n + 1 = 4.358898944 Reorder the terms: 1 + n = 4.358898944 Solving 1 + n = 4.358898944 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 = 4.358898944 + -1 Combine like terms: 1 + -1 = 0 0 + n = 4.358898944 + -1 n = 4.358898944 + -1 Combine like terms: 4.358898944 + -1 = 3.358898944 n = 3.358898944 Simplifying n = 3.358898944Subproblem 2
n + 1 = -4.358898944 Simplifying n + 1 = -4.358898944 Reorder the terms: 1 + n = -4.358898944 Solving 1 + n = -4.358898944 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 = -4.358898944 + -1 Combine like terms: 1 + -1 = 0 0 + n = -4.358898944 + -1 n = -4.358898944 + -1 Combine like terms: -4.358898944 + -1 = -5.358898944 n = -5.358898944 Simplifying n = -5.358898944Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.358898944, -5.358898944}
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