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Simplifying 26n2 + n + 6 = 9 Reorder the terms: 6 + n + 26n2 = 9 Solving 6 + n + 26n2 = 9 Solving for variable 'n'. Reorder the terms: 6 + -9 + n + 26n2 = 9 + -9 Combine like terms: 6 + -9 = -3 -3 + n + 26n2 = 9 + -9 Combine like terms: 9 + -9 = 0 -3 + n + 26n2 = 0 Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. -0.1153846154 + 0.03846153846n + n2 = 0 Move the constant term to the right: Add '0.1153846154' to each side of the equation. -0.1153846154 + 0.03846153846n + 0.1153846154 + n2 = 0 + 0.1153846154 Reorder the terms: -0.1153846154 + 0.1153846154 + 0.03846153846n + n2 = 0 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + 0.03846153846n + n2 = 0 + 0.1153846154 0.03846153846n + n2 = 0 + 0.1153846154 Combine like terms: 0 + 0.1153846154 = 0.1153846154 0.03846153846n + n2 = 0.1153846154 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.03846153846n + 0.25 + n2 = 0.1153846154 + 0.25 Reorder the terms: 0.25 + 0.03846153846n + n2 = 0.1153846154 + 0.25 Combine like terms: 0.1153846154 + 0.25 = 0.3653846154 0.25 + 0.03846153846n + n2 = 0.3653846154 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 0.3653846154 Calculate the square root of the right side: 0.604470525 Break this problem into two subproblems by setting (n + 0.5) equal to 0.604470525 and -0.604470525.Subproblem 1
n + 0.5 = 0.604470525 Simplifying n + 0.5 = 0.604470525 Reorder the terms: 0.5 + n = 0.604470525 Solving 0.5 + n = 0.604470525 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 0.604470525 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 0.604470525 + -0.5 n = 0.604470525 + -0.5 Combine like terms: 0.604470525 + -0.5 = 0.104470525 n = 0.104470525 Simplifying n = 0.104470525Subproblem 2
n + 0.5 = -0.604470525 Simplifying n + 0.5 = -0.604470525 Reorder the terms: 0.5 + n = -0.604470525 Solving 0.5 + n = -0.604470525 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -0.604470525 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -0.604470525 + -0.5 n = -0.604470525 + -0.5 Combine like terms: -0.604470525 + -0.5 = -1.104470525 n = -1.104470525 Simplifying n = -1.104470525Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.104470525, -1.104470525}
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