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Simplifying 4n2 + 7n + -240 = 0 Reorder the terms: -240 + 7n + 4n2 = 0 Solving -240 + 7n + 4n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -60 + 1.75n + n2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 1.75n + 60 + n2 = 0 + 60 Reorder the terms: -60 + 60 + 1.75n + n2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 1.75n + n2 = 0 + 60 1.75n + n2 = 0 + 60 Combine like terms: 0 + 60 = 60 1.75n + n2 = 60 The n term is 1.75n. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75n + 0.765625 + n2 = 60 + 0.765625 Reorder the terms: 0.765625 + 1.75n + n2 = 60 + 0.765625 Combine like terms: 60 + 0.765625 = 60.765625 0.765625 + 1.75n + n2 = 60.765625 Factor a perfect square on the left side: (n + 0.875)(n + 0.875) = 60.765625 Calculate the square root of the right side: 7.795230914 Break this problem into two subproblems by setting (n + 0.875) equal to 7.795230914 and -7.795230914.Subproblem 1
n + 0.875 = 7.795230914 Simplifying n + 0.875 = 7.795230914 Reorder the terms: 0.875 + n = 7.795230914 Solving 0.875 + n = 7.795230914 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + n = 7.795230914 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + n = 7.795230914 + -0.875 n = 7.795230914 + -0.875 Combine like terms: 7.795230914 + -0.875 = 6.920230914 n = 6.920230914 Simplifying n = 6.920230914Subproblem 2
n + 0.875 = -7.795230914 Simplifying n + 0.875 = -7.795230914 Reorder the terms: 0.875 + n = -7.795230914 Solving 0.875 + n = -7.795230914 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + n = -7.795230914 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + n = -7.795230914 + -0.875 n = -7.795230914 + -0.875 Combine like terms: -7.795230914 + -0.875 = -8.670230914 n = -8.670230914 Simplifying n = -8.670230914Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.920230914, -8.670230914}
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