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Simplifying 5n2 + 21n + -1818 = 0 Reorder the terms: -1818 + 21n + 5n2 = 0 Solving -1818 + 21n + 5n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -363.6 + 4.2n + n2 = 0 Move the constant term to the right: Add '363.6' to each side of the equation. -363.6 + 4.2n + 363.6 + n2 = 0 + 363.6 Reorder the terms: -363.6 + 363.6 + 4.2n + n2 = 0 + 363.6 Combine like terms: -363.6 + 363.6 = 0.0 0.0 + 4.2n + n2 = 0 + 363.6 4.2n + n2 = 0 + 363.6 Combine like terms: 0 + 363.6 = 363.6 4.2n + n2 = 363.6 The n term is 4.2n. Take half its coefficient (2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. 4.2n + 4.41 + n2 = 363.6 + 4.41 Reorder the terms: 4.41 + 4.2n + n2 = 363.6 + 4.41 Combine like terms: 363.6 + 4.41 = 368.01 4.41 + 4.2n + n2 = 368.01 Factor a perfect square on the left side: (n + 2.1)(n + 2.1) = 368.01 Calculate the square root of the right side: 19.183586734 Break this problem into two subproblems by setting (n + 2.1) equal to 19.183586734 and -19.183586734.Subproblem 1
n + 2.1 = 19.183586734 Simplifying n + 2.1 = 19.183586734 Reorder the terms: 2.1 + n = 19.183586734 Solving 2.1 + n = 19.183586734 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + n = 19.183586734 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + n = 19.183586734 + -2.1 n = 19.183586734 + -2.1 Combine like terms: 19.183586734 + -2.1 = 17.083586734 n = 17.083586734 Simplifying n = 17.083586734Subproblem 2
n + 2.1 = -19.183586734 Simplifying n + 2.1 = -19.183586734 Reorder the terms: 2.1 + n = -19.183586734 Solving 2.1 + n = -19.183586734 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + n = -19.183586734 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + n = -19.183586734 + -2.1 n = -19.183586734 + -2.1 Combine like terms: -19.183586734 + -2.1 = -21.283586734 n = -21.283586734 Simplifying n = -21.283586734Solution
The solution to the problem is based on the solutions from the subproblems. n = {17.083586734, -21.283586734}
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