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Simplifying 0 = 2n2 + 8n + -9 Reorder the terms: 0 = -9 + 8n + 2n2 Solving 0 = -9 + 8n + 2n2 Solving for variable 'n'. Combine like terms: 0 + 9 = 9 9 + -8n + -2n2 = -9 + 8n + 2n2 + 9 + -8n + -2n2 Reorder the terms: 9 + -8n + -2n2 = -9 + 9 + 8n + -8n + 2n2 + -2n2 Combine like terms: -9 + 9 = 0 9 + -8n + -2n2 = 0 + 8n + -8n + 2n2 + -2n2 9 + -8n + -2n2 = 8n + -8n + 2n2 + -2n2 Combine like terms: 8n + -8n = 0 9 + -8n + -2n2 = 0 + 2n2 + -2n2 9 + -8n + -2n2 = 2n2 + -2n2 Combine like terms: 2n2 + -2n2 = 0 9 + -8n + -2n2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4.5 + 4n + n2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 4n + 4.5 + n2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 4n + n2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 4n + n2 = 0 + 4.5 4n + n2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 4n + n2 = 4.5 The n term is 4n. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4n + 4 + n2 = 4.5 + 4 Reorder the terms: 4 + 4n + n2 = 4.5 + 4 Combine like terms: 4.5 + 4 = 8.5 4 + 4n + n2 = 8.5 Factor a perfect square on the left side: (n + 2)(n + 2) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (n + 2) equal to 2.915475947 and -2.915475947.Subproblem 1
n + 2 = 2.915475947 Simplifying n + 2 = 2.915475947 Reorder the terms: 2 + n = 2.915475947 Solving 2 + n = 2.915475947 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 2.915475947 + -2 Combine like terms: 2 + -2 = 0 0 + n = 2.915475947 + -2 n = 2.915475947 + -2 Combine like terms: 2.915475947 + -2 = 0.915475947 n = 0.915475947 Simplifying n = 0.915475947Subproblem 2
n + 2 = -2.915475947 Simplifying n + 2 = -2.915475947 Reorder the terms: 2 + n = -2.915475947 Solving 2 + n = -2.915475947 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = -2.915475947 + -2 Combine like terms: 2 + -2 = 0 0 + n = -2.915475947 + -2 n = -2.915475947 + -2 Combine like terms: -2.915475947 + -2 = -4.915475947 n = -4.915475947 Simplifying n = -4.915475947Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.915475947, -4.915475947}
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