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Simplifying 2n2 + -5n + -8 = 0 Reorder the terms: -8 + -5n + 2n2 = 0 Solving -8 + -5n + 2n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + -2.5n + n2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -2.5n + 4 + n2 = 0 + 4 Reorder the terms: -4 + 4 + -2.5n + n2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2.5n + n2 = 0 + 4 -2.5n + n2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2.5n + n2 = 4 The n term is -2.5n. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5n + 1.5625 + n2 = 4 + 1.5625 Reorder the terms: 1.5625 + -2.5n + n2 = 4 + 1.5625 Combine like terms: 4 + 1.5625 = 5.5625 1.5625 + -2.5n + n2 = 5.5625 Factor a perfect square on the left side: (n + -1.25)(n + -1.25) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (n + -1.25) equal to 2.358495283 and -2.358495283.Subproblem 1
n + -1.25 = 2.358495283 Simplifying n + -1.25 = 2.358495283 Reorder the terms: -1.25 + n = 2.358495283 Solving -1.25 + n = 2.358495283 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + n = 2.358495283 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + n = 2.358495283 + 1.25 n = 2.358495283 + 1.25 Combine like terms: 2.358495283 + 1.25 = 3.608495283 n = 3.608495283 Simplifying n = 3.608495283Subproblem 2
n + -1.25 = -2.358495283 Simplifying n + -1.25 = -2.358495283 Reorder the terms: -1.25 + n = -2.358495283 Solving -1.25 + n = -2.358495283 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + n = -2.358495283 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + n = -2.358495283 + 1.25 n = -2.358495283 + 1.25 Combine like terms: -2.358495283 + 1.25 = -1.108495283 n = -1.108495283 Simplifying n = -1.108495283Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.608495283, -1.108495283}
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