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Simplifying 8n2 + -9n + -18 = 0 Reorder the terms: -18 + -9n + 8n2 = 0 Solving -18 + -9n + 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'. -2.25 + -1.125n + n2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -1.125n + 2.25 + n2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -1.125n + n2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -1.125n + n2 = 0 + 2.25 -1.125n + n2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -1.125n + n2 = 2.25 The n term is -1.125n. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125n + 0.31640625 + n2 = 2.25 + 0.31640625 Reorder the terms: 0.31640625 + -1.125n + n2 = 2.25 + 0.31640625 Combine like terms: 2.25 + 0.31640625 = 2.56640625 0.31640625 + -1.125n + n2 = 2.56640625 Factor a perfect square on the left side: (n + -0.5625)(n + -0.5625) = 2.56640625 Calculate the square root of the right side: 1.602000702 Break this problem into two subproblems by setting (n + -0.5625) equal to 1.602000702 and -1.602000702.Subproblem 1
n + -0.5625 = 1.602000702 Simplifying n + -0.5625 = 1.602000702 Reorder the terms: -0.5625 + n = 1.602000702 Solving -0.5625 + n = 1.602000702 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + n = 1.602000702 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + n = 1.602000702 + 0.5625 n = 1.602000702 + 0.5625 Combine like terms: 1.602000702 + 0.5625 = 2.164500702 n = 2.164500702 Simplifying n = 2.164500702Subproblem 2
n + -0.5625 = -1.602000702 Simplifying n + -0.5625 = -1.602000702 Reorder the terms: -0.5625 + n = -1.602000702 Solving -0.5625 + n = -1.602000702 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + n = -1.602000702 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + n = -1.602000702 + 0.5625 n = -1.602000702 + 0.5625 Combine like terms: -1.602000702 + 0.5625 = -1.039500702 n = -1.039500702 Simplifying n = -1.039500702Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.164500702, -1.039500702}
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