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Simplifying 4n2 + -16 = 7n Reorder the terms: -16 + 4n2 = 7n Solving -16 + 4n2 = 7n Solving for variable 'n'. Reorder the terms: -16 + -7n + 4n2 = 7n + -7n Combine like terms: 7n + -7n = 0 -16 + -7n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4 + -1.75n + n2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.75n + 4 + n2 = 0 + 4 Reorder the terms: -4 + 4 + -1.75n + n2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.75n + n2 = 0 + 4 -1.75n + n2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.75n + n2 = 4 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 = 4 + 0.765625 Reorder the terms: 0.765625 + -1.75n + n2 = 4 + 0.765625 Combine like terms: 4 + 0.765625 = 4.765625 0.765625 + -1.75n + n2 = 4.765625 Factor a perfect square on the left side: (n + -0.875)(n + -0.875) = 4.765625 Calculate the square root of the right side: 2.18303115 Break this problem into two subproblems by setting (n + -0.875) equal to 2.18303115 and -2.18303115.Subproblem 1
n + -0.875 = 2.18303115 Simplifying n + -0.875 = 2.18303115 Reorder the terms: -0.875 + n = 2.18303115 Solving -0.875 + n = 2.18303115 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 = 2.18303115 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + n = 2.18303115 + 0.875 n = 2.18303115 + 0.875 Combine like terms: 2.18303115 + 0.875 = 3.05803115 n = 3.05803115 Simplifying n = 3.05803115Subproblem 2
n + -0.875 = -2.18303115 Simplifying n + -0.875 = -2.18303115 Reorder the terms: -0.875 + n = -2.18303115 Solving -0.875 + n = -2.18303115 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 = -2.18303115 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + n = -2.18303115 + 0.875 n = -2.18303115 + 0.875 Combine like terms: -2.18303115 + 0.875 = -1.30803115 n = -1.30803115 Simplifying n = -1.30803115Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.05803115, -1.30803115}
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