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Simplifying 8n2 + -7n + -2 = 0 Reorder the terms: -2 + -7n + 8n2 = 0 Solving -2 + -7n + 8n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.25 + -0.875n + n2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.875n + 0.25 + n2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.875n + n2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.875n + n2 = 0 + 0.25 -0.875n + n2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.875n + n2 = 0.25 The n term is -0.875n. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875n + 0.19140625 + n2 = 0.25 + 0.19140625 Reorder the terms: 0.19140625 + -0.875n + n2 = 0.25 + 0.19140625 Combine like terms: 0.25 + 0.19140625 = 0.44140625 0.19140625 + -0.875n + n2 = 0.44140625 Factor a perfect square on the left side: (n + -0.4375)(n + -0.4375) = 0.44140625 Calculate the square root of the right side: 0.664384113 Break this problem into two subproblems by setting (n + -0.4375) equal to 0.664384113 and -0.664384113.Subproblem 1
n + -0.4375 = 0.664384113 Simplifying n + -0.4375 = 0.664384113 Reorder the terms: -0.4375 + n = 0.664384113 Solving -0.4375 + n = 0.664384113 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + n = 0.664384113 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + n = 0.664384113 + 0.4375 n = 0.664384113 + 0.4375 Combine like terms: 0.664384113 + 0.4375 = 1.101884113 n = 1.101884113 Simplifying n = 1.101884113Subproblem 2
n + -0.4375 = -0.664384113 Simplifying n + -0.4375 = -0.664384113 Reorder the terms: -0.4375 + n = -0.664384113 Solving -0.4375 + n = -0.664384113 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + n = -0.664384113 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + n = -0.664384113 + 0.4375 n = -0.664384113 + 0.4375 Combine like terms: -0.664384113 + 0.4375 = -0.226884113 n = -0.226884113 Simplifying n = -0.226884113Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.101884113, -0.226884113}
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