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Simplifying 8n2 + -11n + -15 = 0 Reorder the terms: -15 + -11n + 8n2 = 0 Solving -15 + -11n + 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'. -1.875 + -1.375n + n2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -1.375n + 1.875 + n2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -1.375n + n2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -1.375n + n2 = 0 + 1.875 -1.375n + n2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -1.375n + n2 = 1.875 The n term is -1.375n. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375n + 0.47265625 + n2 = 1.875 + 0.47265625 Reorder the terms: 0.47265625 + -1.375n + n2 = 1.875 + 0.47265625 Combine like terms: 1.875 + 0.47265625 = 2.34765625 0.47265625 + -1.375n + n2 = 2.34765625 Factor a perfect square on the left side: (n + -0.6875)(n + -0.6875) = 2.34765625 Calculate the square root of the right side: 1.532206334 Break this problem into two subproblems by setting (n + -0.6875) equal to 1.532206334 and -1.532206334.Subproblem 1
n + -0.6875 = 1.532206334 Simplifying n + -0.6875 = 1.532206334 Reorder the terms: -0.6875 + n = 1.532206334 Solving -0.6875 + n = 1.532206334 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + n = 1.532206334 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + n = 1.532206334 + 0.6875 n = 1.532206334 + 0.6875 Combine like terms: 1.532206334 + 0.6875 = 2.219706334 n = 2.219706334 Simplifying n = 2.219706334Subproblem 2
n + -0.6875 = -1.532206334 Simplifying n + -0.6875 = -1.532206334 Reorder the terms: -0.6875 + n = -1.532206334 Solving -0.6875 + n = -1.532206334 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + n = -1.532206334 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + n = -1.532206334 + 0.6875 n = -1.532206334 + 0.6875 Combine like terms: -1.532206334 + 0.6875 = -0.844706334 n = -0.844706334 Simplifying n = -0.844706334Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.219706334, -0.844706334}
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