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Simplifying 10n2 + 80n + -262.5 = 0 Reorder the terms: -262.5 + 80n + 10n2 = 0 Solving -262.5 + 80n + 10n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -26.25 + 8n + n2 = 0 Move the constant term to the right: Add '26.25' to each side of the equation. -26.25 + 8n + 26.25 + n2 = 0 + 26.25 Reorder the terms: -26.25 + 26.25 + 8n + n2 = 0 + 26.25 Combine like terms: -26.25 + 26.25 = 0.00 0.00 + 8n + n2 = 0 + 26.25 8n + n2 = 0 + 26.25 Combine like terms: 0 + 26.25 = 26.25 8n + n2 = 26.25 The n term is 8n. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8n + 16 + n2 = 26.25 + 16 Reorder the terms: 16 + 8n + n2 = 26.25 + 16 Combine like terms: 26.25 + 16 = 42.25 16 + 8n + n2 = 42.25 Factor a perfect square on the left side: (n + 4)(n + 4) = 42.25 Calculate the square root of the right side: 6.5 Break this problem into two subproblems by setting (n + 4) equal to 6.5 and -6.5.Subproblem 1
n + 4 = 6.5 Simplifying n + 4 = 6.5 Reorder the terms: 4 + n = 6.5 Solving 4 + n = 6.5 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = 6.5 + -4 Combine like terms: 4 + -4 = 0 0 + n = 6.5 + -4 n = 6.5 + -4 Combine like terms: 6.5 + -4 = 2.5 n = 2.5 Simplifying n = 2.5Subproblem 2
n + 4 = -6.5 Simplifying n + 4 = -6.5 Reorder the terms: 4 + n = -6.5 Solving 4 + n = -6.5 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = -6.5 + -4 Combine like terms: 4 + -4 = 0 0 + n = -6.5 + -4 n = -6.5 + -4 Combine like terms: -6.5 + -4 = -10.5 n = -10.5 Simplifying n = -10.5Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.5, -10.5}
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