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Simplifying -5n2 + -2n + 10 = 0 Reorder the terms: 10 + -2n + -5n2 = 0 Solving 10 + -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'. -2 + 0.4n + n2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.4n + 2 + n2 = 0 + 2 Reorder the terms: -2 + 2 + 0.4n + n2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.4n + n2 = 0 + 2 0.4n + n2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.4n + n2 = 2 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 = 2 + 0.04 Reorder the terms: 0.04 + 0.4n + n2 = 2 + 0.04 Combine like terms: 2 + 0.04 = 2.04 0.04 + 0.4n + n2 = 2.04 Factor a perfect square on the left side: (n + 0.2)(n + 0.2) = 2.04 Calculate the square root of the right side: 1.428285686 Break this problem into two subproblems by setting (n + 0.2) equal to 1.428285686 and -1.428285686.Subproblem 1
n + 0.2 = 1.428285686 Simplifying n + 0.2 = 1.428285686 Reorder the terms: 0.2 + n = 1.428285686 Solving 0.2 + n = 1.428285686 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 = 1.428285686 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + n = 1.428285686 + -0.2 n = 1.428285686 + -0.2 Combine like terms: 1.428285686 + -0.2 = 1.228285686 n = 1.228285686 Simplifying n = 1.228285686Subproblem 2
n + 0.2 = -1.428285686 Simplifying n + 0.2 = -1.428285686 Reorder the terms: 0.2 + n = -1.428285686 Solving 0.2 + n = -1.428285686 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 = -1.428285686 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + n = -1.428285686 + -0.2 n = -1.428285686 + -0.2 Combine like terms: -1.428285686 + -0.2 = -1.628285686 n = -1.628285686 Simplifying n = -1.628285686Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.228285686, -1.628285686}
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