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Simplifying -5n2 + -26n + 48 = 0 Reorder the terms: 48 + -26n + -5n2 = 0 Solving 48 + -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'. -9.6 + 5.2n + n2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + 5.2n + 9.6 + n2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + 5.2n + n2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + 5.2n + n2 = 0 + 9.6 5.2n + n2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 5.2n + n2 = 9.6 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 = 9.6 + 6.76 Reorder the terms: 6.76 + 5.2n + n2 = 9.6 + 6.76 Combine like terms: 9.6 + 6.76 = 16.36 6.76 + 5.2n + n2 = 16.36 Factor a perfect square on the left side: (n + 2.6)(n + 2.6) = 16.36 Calculate the square root of the right side: 4.044749683 Break this problem into two subproblems by setting (n + 2.6) equal to 4.044749683 and -4.044749683.Subproblem 1
n + 2.6 = 4.044749683 Simplifying n + 2.6 = 4.044749683 Reorder the terms: 2.6 + n = 4.044749683 Solving 2.6 + n = 4.044749683 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 = 4.044749683 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + n = 4.044749683 + -2.6 n = 4.044749683 + -2.6 Combine like terms: 4.044749683 + -2.6 = 1.444749683 n = 1.444749683 Simplifying n = 1.444749683Subproblem 2
n + 2.6 = -4.044749683 Simplifying n + 2.6 = -4.044749683 Reorder the terms: 2.6 + n = -4.044749683 Solving 2.6 + n = -4.044749683 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 = -4.044749683 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + n = -4.044749683 + -2.6 n = -4.044749683 + -2.6 Combine like terms: -4.044749683 + -2.6 = -6.644749683 n = -6.644749683 Simplifying n = -6.644749683Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.444749683, -6.644749683}
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