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Simplifying -5n2 + -26n + 40 = 0 Reorder the terms: 40 + -26n + -5n2 = 0 Solving 40 + -26n + -5n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -8 + 5.2n + n2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 5.2n + 8 + n2 = 0 + 8 Reorder the terms: -8 + 8 + 5.2n + n2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 5.2n + n2 = 0 + 8 5.2n + n2 = 0 + 8 Combine like terms: 0 + 8 = 8 5.2n + n2 = 8 The n term is 5.2n. Take half its coefficient (2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. 5.2n + 6.76 + n2 = 8 + 6.76 Reorder the terms: 6.76 + 5.2n + n2 = 8 + 6.76 Combine like terms: 8 + 6.76 = 14.76 6.76 + 5.2n + n2 = 14.76 Factor a perfect square on the left side: (n + 2.6)(n + 2.6) = 14.76 Calculate the square root of the right side: 3.841874542 Break this problem into two subproblems by setting (n + 2.6) equal to 3.841874542 and -3.841874542.Subproblem 1
n + 2.6 = 3.841874542 Simplifying n + 2.6 = 3.841874542 Reorder the terms: 2.6 + n = 3.841874542 Solving 2.6 + n = 3.841874542 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + n = 3.841874542 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + n = 3.841874542 + -2.6 n = 3.841874542 + -2.6 Combine like terms: 3.841874542 + -2.6 = 1.241874542 n = 1.241874542 Simplifying n = 1.241874542Subproblem 2
n + 2.6 = -3.841874542 Simplifying n + 2.6 = -3.841874542 Reorder the terms: 2.6 + n = -3.841874542 Solving 2.6 + n = -3.841874542 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + n = -3.841874542 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + n = -3.841874542 + -2.6 n = -3.841874542 + -2.6 Combine like terms: -3.841874542 + -2.6 = -6.441874542 n = -6.441874542 Simplifying n = -6.441874542Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.241874542, -6.441874542}
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