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Simplifying 8n2 + -5n + -5 = 0 Reorder the terms: -5 + -5n + 8n2 = 0 Solving -5 + -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'. -0.625 + -0.625n + n2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -0.625n + 0.625 + n2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -0.625n + n2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -0.625n + n2 = 0 + 0.625 -0.625n + n2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -0.625n + n2 = 0.625 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 = 0.625 + 0.09765625 Reorder the terms: 0.09765625 + -0.625n + n2 = 0.625 + 0.09765625 Combine like terms: 0.625 + 0.09765625 = 0.72265625 0.09765625 + -0.625n + n2 = 0.72265625 Factor a perfect square on the left side: (n + -0.3125)(n + -0.3125) = 0.72265625 Calculate the square root of the right side: 0.850091907 Break this problem into two subproblems by setting (n + -0.3125) equal to 0.850091907 and -0.850091907.Subproblem 1
n + -0.3125 = 0.850091907 Simplifying n + -0.3125 = 0.850091907 Reorder the terms: -0.3125 + n = 0.850091907 Solving -0.3125 + n = 0.850091907 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 = 0.850091907 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + n = 0.850091907 + 0.3125 n = 0.850091907 + 0.3125 Combine like terms: 0.850091907 + 0.3125 = 1.162591907 n = 1.162591907 Simplifying n = 1.162591907Subproblem 2
n + -0.3125 = -0.850091907 Simplifying n + -0.3125 = -0.850091907 Reorder the terms: -0.3125 + n = -0.850091907 Solving -0.3125 + n = -0.850091907 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 = -0.850091907 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + n = -0.850091907 + 0.3125 n = -0.850091907 + 0.3125 Combine like terms: -0.850091907 + 0.3125 = -0.537591907 n = -0.537591907 Simplifying n = -0.537591907Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.162591907, -0.537591907}
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