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Simplifying n2 + -8n + -6 = n Reorder the terms: -6 + -8n + n2 = n Solving -6 + -8n + n2 = n Solving for variable 'n'. Reorder the terms: -6 + -8n + -1n + n2 = n + -1n Combine like terms: -8n + -1n = -9n -6 + -9n + n2 = n + -1n Combine like terms: n + -1n = 0 -6 + -9n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -9n + 6 + n2 = 0 + 6 Reorder the terms: -6 + 6 + -9n + n2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -9n + n2 = 0 + 6 -9n + n2 = 0 + 6 Combine like terms: 0 + 6 = 6 -9n + n2 = 6 The n term is -9n. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9n + 20.25 + n2 = 6 + 20.25 Reorder the terms: 20.25 + -9n + n2 = 6 + 20.25 Combine like terms: 6 + 20.25 = 26.25 20.25 + -9n + n2 = 26.25 Factor a perfect square on the left side: (n + -4.5)(n + -4.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (n + -4.5) equal to 5.123475383 and -5.123475383.Subproblem 1
n + -4.5 = 5.123475383 Simplifying n + -4.5 = 5.123475383 Reorder the terms: -4.5 + n = 5.123475383 Solving -4.5 + n = 5.123475383 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = 5.123475383 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = 5.123475383 + 4.5 n = 5.123475383 + 4.5 Combine like terms: 5.123475383 + 4.5 = 9.623475383 n = 9.623475383 Simplifying n = 9.623475383Subproblem 2
n + -4.5 = -5.123475383 Simplifying n + -4.5 = -5.123475383 Reorder the terms: -4.5 + n = -5.123475383 Solving -4.5 + n = -5.123475383 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = -5.123475383 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = -5.123475383 + 4.5 n = -5.123475383 + 4.5 Combine like terms: -5.123475383 + 4.5 = -0.623475383 n = -0.623475383 Simplifying n = -0.623475383Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.623475383, -0.623475383}
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