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Simplifying 7n2 + 20n + -48 = 0 Reorder the terms: -48 + 20n + 7n2 = 0 Solving -48 + 20n + 7n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -6.857142857 + 2.857142857n + n2 = 0 Move the constant term to the right: Add '6.857142857' to each side of the equation. -6.857142857 + 2.857142857n + 6.857142857 + n2 = 0 + 6.857142857 Reorder the terms: -6.857142857 + 6.857142857 + 2.857142857n + n2 = 0 + 6.857142857 Combine like terms: -6.857142857 + 6.857142857 = 0.000000000 0.000000000 + 2.857142857n + n2 = 0 + 6.857142857 2.857142857n + n2 = 0 + 6.857142857 Combine like terms: 0 + 6.857142857 = 6.857142857 2.857142857n + n2 = 6.857142857 The n term is 2.857142857n. Take half its coefficient (1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. 2.857142857n + 2.040816328 + n2 = 6.857142857 + 2.040816328 Reorder the terms: 2.040816328 + 2.857142857n + n2 = 6.857142857 + 2.040816328 Combine like terms: 6.857142857 + 2.040816328 = 8.897959185 2.040816328 + 2.857142857n + n2 = 8.897959185 Factor a perfect square on the left side: (n + 1.428571429)(n + 1.428571429) = 8.897959185 Calculate the square root of the right side: 2.982944717 Break this problem into two subproblems by setting (n + 1.428571429) equal to 2.982944717 and -2.982944717.Subproblem 1
n + 1.428571429 = 2.982944717 Simplifying n + 1.428571429 = 2.982944717 Reorder the terms: 1.428571429 + n = 2.982944717 Solving 1.428571429 + n = 2.982944717 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + n = 2.982944717 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + n = 2.982944717 + -1.428571429 n = 2.982944717 + -1.428571429 Combine like terms: 2.982944717 + -1.428571429 = 1.554373288 n = 1.554373288 Simplifying n = 1.554373288Subproblem 2
n + 1.428571429 = -2.982944717 Simplifying n + 1.428571429 = -2.982944717 Reorder the terms: 1.428571429 + n = -2.982944717 Solving 1.428571429 + n = -2.982944717 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + n = -2.982944717 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + n = -2.982944717 + -1.428571429 n = -2.982944717 + -1.428571429 Combine like terms: -2.982944717 + -1.428571429 = -4.411516146 n = -4.411516146 Simplifying n = -4.411516146Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.554373288, -4.411516146}
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