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Simplifying 8n2 + 5n + -636 = 0 Reorder the terms: -636 + 5n + 8n2 = 0 Solving -636 + 5n + 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'. -79.5 + 0.625n + n2 = 0 Move the constant term to the right: Add '79.5' to each side of the equation. -79.5 + 0.625n + 79.5 + n2 = 0 + 79.5 Reorder the terms: -79.5 + 79.5 + 0.625n + n2 = 0 + 79.5 Combine like terms: -79.5 + 79.5 = 0.0 0.0 + 0.625n + n2 = 0 + 79.5 0.625n + n2 = 0 + 79.5 Combine like terms: 0 + 79.5 = 79.5 0.625n + n2 = 79.5 The n term is 0.625n. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625n + 0.09765625 + n2 = 79.5 + 0.09765625 Reorder the terms: 0.09765625 + 0.625n + n2 = 79.5 + 0.09765625 Combine like terms: 79.5 + 0.09765625 = 79.59765625 0.09765625 + 0.625n + n2 = 79.59765625 Factor a perfect square on the left side: (n + 0.3125)(n + 0.3125) = 79.59765625 Calculate the square root of the right side: 8.92175186 Break this problem into two subproblems by setting (n + 0.3125) equal to 8.92175186 and -8.92175186.Subproblem 1
n + 0.3125 = 8.92175186 Simplifying n + 0.3125 = 8.92175186 Reorder the terms: 0.3125 + n = 8.92175186 Solving 0.3125 + n = 8.92175186 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + n = 8.92175186 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + n = 8.92175186 + -0.3125 n = 8.92175186 + -0.3125 Combine like terms: 8.92175186 + -0.3125 = 8.60925186 n = 8.60925186 Simplifying n = 8.60925186Subproblem 2
n + 0.3125 = -8.92175186 Simplifying n + 0.3125 = -8.92175186 Reorder the terms: 0.3125 + n = -8.92175186 Solving 0.3125 + n = -8.92175186 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + n = -8.92175186 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + n = -8.92175186 + -0.3125 n = -8.92175186 + -0.3125 Combine like terms: -8.92175186 + -0.3125 = -9.23425186 n = -9.23425186 Simplifying n = -9.23425186Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.60925186, -9.23425186}
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