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Simplifying 8n2 + -77n + 7 = 0 Reorder the terms: 7 + -77n + 8n2 = 0 Solving 7 + -77n + 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'. 0.875 + -9.625n + n2 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + -9.625n + -0.875 + n2 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + -9.625n + n2 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + -9.625n + n2 = 0 + -0.875 -9.625n + n2 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 -9.625n + n2 = -0.875 The n term is -9.625n. Take half its coefficient (-4.8125). Square it (23.16015625) and add it to both sides. Add '23.16015625' to each side of the equation. -9.625n + 23.16015625 + n2 = -0.875 + 23.16015625 Reorder the terms: 23.16015625 + -9.625n + n2 = -0.875 + 23.16015625 Combine like terms: -0.875 + 23.16015625 = 22.28515625 23.16015625 + -9.625n + n2 = 22.28515625 Factor a perfect square on the left side: (n + -4.8125)(n + -4.8125) = 22.28515625 Calculate the square root of the right side: 4.72071565 Break this problem into two subproblems by setting (n + -4.8125) equal to 4.72071565 and -4.72071565.Subproblem 1
n + -4.8125 = 4.72071565 Simplifying n + -4.8125 = 4.72071565 Reorder the terms: -4.8125 + n = 4.72071565 Solving -4.8125 + n = 4.72071565 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.8125' to each side of the equation. -4.8125 + 4.8125 + n = 4.72071565 + 4.8125 Combine like terms: -4.8125 + 4.8125 = 0.0000 0.0000 + n = 4.72071565 + 4.8125 n = 4.72071565 + 4.8125 Combine like terms: 4.72071565 + 4.8125 = 9.53321565 n = 9.53321565 Simplifying n = 9.53321565Subproblem 2
n + -4.8125 = -4.72071565 Simplifying n + -4.8125 = -4.72071565 Reorder the terms: -4.8125 + n = -4.72071565 Solving -4.8125 + n = -4.72071565 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.8125' to each side of the equation. -4.8125 + 4.8125 + n = -4.72071565 + 4.8125 Combine like terms: -4.8125 + 4.8125 = 0.0000 0.0000 + n = -4.72071565 + 4.8125 n = -4.72071565 + 4.8125 Combine like terms: -4.72071565 + 4.8125 = 0.09178435 n = 0.09178435 Simplifying n = 0.09178435Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.53321565, 0.09178435}
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