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Simplifying 5n2 + -2n + -728 = 0 Reorder the terms: -728 + -2n + 5n2 = 0 Solving -728 + -2n + 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'. -145.6 + -0.4n + n2 = 0 Move the constant term to the right: Add '145.6' to each side of the equation. -145.6 + -0.4n + 145.6 + n2 = 0 + 145.6 Reorder the terms: -145.6 + 145.6 + -0.4n + n2 = 0 + 145.6 Combine like terms: -145.6 + 145.6 = 0.0 0.0 + -0.4n + n2 = 0 + 145.6 -0.4n + n2 = 0 + 145.6 Combine like terms: 0 + 145.6 = 145.6 -0.4n + n2 = 145.6 The n term is -0.4n. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4n + 0.04 + n2 = 145.6 + 0.04 Reorder the terms: 0.04 + -0.4n + n2 = 145.6 + 0.04 Combine like terms: 145.6 + 0.04 = 145.64 0.04 + -0.4n + n2 = 145.64 Factor a perfect square on the left side: (n + -0.2)(n + -0.2) = 145.64 Calculate the square root of the right side: 12.068139873 Break this problem into two subproblems by setting (n + -0.2) equal to 12.068139873 and -12.068139873.Subproblem 1
n + -0.2 = 12.068139873 Simplifying n + -0.2 = 12.068139873 Reorder the terms: -0.2 + n = 12.068139873 Solving -0.2 + n = 12.068139873 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + n = 12.068139873 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + n = 12.068139873 + 0.2 n = 12.068139873 + 0.2 Combine like terms: 12.068139873 + 0.2 = 12.268139873 n = 12.268139873 Simplifying n = 12.268139873Subproblem 2
n + -0.2 = -12.068139873 Simplifying n + -0.2 = -12.068139873 Reorder the terms: -0.2 + n = -12.068139873 Solving -0.2 + n = -12.068139873 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + n = -12.068139873 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + n = -12.068139873 + 0.2 n = -12.068139873 + 0.2 Combine like terms: -12.068139873 + 0.2 = -11.868139873 n = -11.868139873 Simplifying n = -11.868139873Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.268139873, -11.868139873}
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