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Simplifying n + n + n + n + n + n + n = n2 + -4 Combine like terms: n + n = 2n 2n + n + n + n + n + n = n2 + -4 Combine like terms: 2n + n = 3n 3n + n + n + n + n = n2 + -4 Combine like terms: 3n + n = 4n 4n + n + n + n = n2 + -4 Combine like terms: 4n + n = 5n 5n + n + n = n2 + -4 Combine like terms: 5n + n = 6n 6n + n = n2 + -4 Combine like terms: 6n + n = 7n 7n = n2 + -4 Reorder the terms: 7n = -4 + n2 Solving 7n = -4 + n2 Solving for variable 'n'. Reorder the terms: 4 + 7n + -1n2 = -4 + n2 + 4 + -1n2 Reorder the terms: 4 + 7n + -1n2 = -4 + 4 + n2 + -1n2 Combine like terms: -4 + 4 = 0 4 + 7n + -1n2 = 0 + n2 + -1n2 4 + 7n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 4 + 7n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -7n + n2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -7n + 4 + n2 = 0 + 4 Reorder the terms: -4 + 4 + -7n + n2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7n + n2 = 0 + 4 -7n + n2 = 0 + 4 Combine like terms: 0 + 4 = 4 -7n + n2 = 4 The n term is -7n. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7n + 12.25 + n2 = 4 + 12.25 Reorder the terms: 12.25 + -7n + n2 = 4 + 12.25 Combine like terms: 4 + 12.25 = 16.25 12.25 + -7n + n2 = 16.25 Factor a perfect square on the left side: (n + -3.5)(n + -3.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (n + -3.5) equal to 4.031128874 and -4.031128874.Subproblem 1
n + -3.5 = 4.031128874 Simplifying n + -3.5 = 4.031128874 Reorder the terms: -3.5 + n = 4.031128874 Solving -3.5 + n = 4.031128874 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + n = 4.031128874 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + n = 4.031128874 + 3.5 n = 4.031128874 + 3.5 Combine like terms: 4.031128874 + 3.5 = 7.531128874 n = 7.531128874 Simplifying n = 7.531128874Subproblem 2
n + -3.5 = -4.031128874 Simplifying n + -3.5 = -4.031128874 Reorder the terms: -3.5 + n = -4.031128874 Solving -3.5 + n = -4.031128874 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + n = -4.031128874 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + n = -4.031128874 + 3.5 n = -4.031128874 + 3.5 Combine like terms: -4.031128874 + 3.5 = -0.531128874 n = -0.531128874 Simplifying n = -0.531128874Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.531128874, -0.531128874}
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