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Simplifying 8n2 + -53n + -56 = 0 Reorder the terms: -56 + -53n + 8n2 = 0 Solving -56 + -53n + 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'. -7 + -6.625n + n2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -6.625n + 7 + n2 = 0 + 7 Reorder the terms: -7 + 7 + -6.625n + n2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6.625n + n2 = 0 + 7 -6.625n + n2 = 0 + 7 Combine like terms: 0 + 7 = 7 -6.625n + n2 = 7 The n term is -6.625n. Take half its coefficient (-3.3125). Square it (10.97265625) and add it to both sides. Add '10.97265625' to each side of the equation. -6.625n + 10.97265625 + n2 = 7 + 10.97265625 Reorder the terms: 10.97265625 + -6.625n + n2 = 7 + 10.97265625 Combine like terms: 7 + 10.97265625 = 17.97265625 10.97265625 + -6.625n + n2 = 17.97265625 Factor a perfect square on the left side: (n + -3.3125)(n + -3.3125) = 17.97265625 Calculate the square root of the right side: 4.239416971 Break this problem into two subproblems by setting (n + -3.3125) equal to 4.239416971 and -4.239416971.Subproblem 1
n + -3.3125 = 4.239416971 Simplifying n + -3.3125 = 4.239416971 Reorder the terms: -3.3125 + n = 4.239416971 Solving -3.3125 + n = 4.239416971 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.3125' to each side of the equation. -3.3125 + 3.3125 + n = 4.239416971 + 3.3125 Combine like terms: -3.3125 + 3.3125 = 0.0000 0.0000 + n = 4.239416971 + 3.3125 n = 4.239416971 + 3.3125 Combine like terms: 4.239416971 + 3.3125 = 7.551916971 n = 7.551916971 Simplifying n = 7.551916971Subproblem 2
n + -3.3125 = -4.239416971 Simplifying n + -3.3125 = -4.239416971 Reorder the terms: -3.3125 + n = -4.239416971 Solving -3.3125 + n = -4.239416971 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.3125' to each side of the equation. -3.3125 + 3.3125 + n = -4.239416971 + 3.3125 Combine like terms: -3.3125 + 3.3125 = 0.0000 0.0000 + n = -4.239416971 + 3.3125 n = -4.239416971 + 3.3125 Combine like terms: -4.239416971 + 3.3125 = -0.926916971 n = -0.926916971 Simplifying n = -0.926916971Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.551916971, -0.926916971}
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