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Simplifying 7n2 + -2n + -21 = -5 Reorder the terms: -21 + -2n + 7n2 = -5 Solving -21 + -2n + 7n2 = -5 Solving for variable 'n'. Reorder the terms: -21 + 5 + -2n + 7n2 = -5 + 5 Combine like terms: -21 + 5 = -16 -16 + -2n + 7n2 = -5 + 5 Combine like terms: -5 + 5 = 0 -16 + -2n + 7n2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.285714286 + -0.2857142857n + n2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + -0.2857142857n + 2.285714286 + n2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + -0.2857142857n + n2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + -0.2857142857n + n2 = 0 + 2.285714286 -0.2857142857n + n2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 -0.2857142857n + n2 = 2.285714286 The n term is -0.2857142857n. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857n + 0.02040816328 + n2 = 2.285714286 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857n + n2 = 2.285714286 + 0.02040816328 Combine like terms: 2.285714286 + 0.02040816328 = 2.30612244928 0.02040816328 + -0.2857142857n + n2 = 2.30612244928 Factor a perfect square on the left side: (n + -0.1428571429)(n + -0.1428571429) = 2.30612244928 Calculate the square root of the right side: 1.518592259 Break this problem into two subproblems by setting (n + -0.1428571429) equal to 1.518592259 and -1.518592259.Subproblem 1
n + -0.1428571429 = 1.518592259 Simplifying n + -0.1428571429 = 1.518592259 Reorder the terms: -0.1428571429 + n = 1.518592259 Solving -0.1428571429 + n = 1.518592259 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + n = 1.518592259 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + n = 1.518592259 + 0.1428571429 n = 1.518592259 + 0.1428571429 Combine like terms: 1.518592259 + 0.1428571429 = 1.6614494019 n = 1.6614494019 Simplifying n = 1.6614494019Subproblem 2
n + -0.1428571429 = -1.518592259 Simplifying n + -0.1428571429 = -1.518592259 Reorder the terms: -0.1428571429 + n = -1.518592259 Solving -0.1428571429 + n = -1.518592259 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + n = -1.518592259 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + n = -1.518592259 + 0.1428571429 n = -1.518592259 + 0.1428571429 Combine like terms: -1.518592259 + 0.1428571429 = -1.3757351161 n = -1.3757351161 Simplifying n = -1.3757351161Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.6614494019, -1.3757351161}
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