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Simplifying 7n2 + -15 = -4n Reorder the terms: -15 + 7n2 = -4n Solving -15 + 7n2 = -4n Solving for variable 'n'. Reorder the terms: -15 + 4n + 7n2 = -4n + 4n Combine like terms: -4n + 4n = 0 -15 + 4n + 7n2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.142857143 + 0.5714285714n + n2 = 0 Move the constant term to the right: Add '2.142857143' to each side of the equation. -2.142857143 + 0.5714285714n + 2.142857143 + n2 = 0 + 2.142857143 Reorder the terms: -2.142857143 + 2.142857143 + 0.5714285714n + n2 = 0 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + 0.5714285714n + n2 = 0 + 2.142857143 0.5714285714n + n2 = 0 + 2.142857143 Combine like terms: 0 + 2.142857143 = 2.142857143 0.5714285714n + n2 = 2.142857143 The n term is 0.5714285714n. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714n + 0.08163265305 + n2 = 2.142857143 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714n + n2 = 2.142857143 + 0.08163265305 Combine like terms: 2.142857143 + 0.08163265305 = 2.22448979605 0.08163265305 + 0.5714285714n + n2 = 2.22448979605 Factor a perfect square on the left side: (n + 0.2857142857)(n + 0.2857142857) = 2.22448979605 Calculate the square root of the right side: 1.491472358 Break this problem into two subproblems by setting (n + 0.2857142857) equal to 1.491472358 and -1.491472358.Subproblem 1
n + 0.2857142857 = 1.491472358 Simplifying n + 0.2857142857 = 1.491472358 Reorder the terms: 0.2857142857 + n = 1.491472358 Solving 0.2857142857 + n = 1.491472358 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + n = 1.491472358 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + n = 1.491472358 + -0.2857142857 n = 1.491472358 + -0.2857142857 Combine like terms: 1.491472358 + -0.2857142857 = 1.2057580723 n = 1.2057580723 Simplifying n = 1.2057580723Subproblem 2
n + 0.2857142857 = -1.491472358 Simplifying n + 0.2857142857 = -1.491472358 Reorder the terms: 0.2857142857 + n = -1.491472358 Solving 0.2857142857 + n = -1.491472358 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + n = -1.491472358 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + n = -1.491472358 + -0.2857142857 n = -1.491472358 + -0.2857142857 Combine like terms: -1.491472358 + -0.2857142857 = -1.7771866437 n = -1.7771866437 Simplifying n = -1.7771866437Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.2057580723, -1.7771866437}
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