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Simplifying n2 = -4n + 13 Reorder the terms: n2 = 13 + -4n Solving n2 = 13 + -4n Solving for variable 'n'. Reorder the terms: -13 + 4n + n2 = 13 + -4n + -13 + 4n Reorder the terms: -13 + 4n + n2 = 13 + -13 + -4n + 4n Combine like terms: 13 + -13 = 0 -13 + 4n + n2 = 0 + -4n + 4n -13 + 4n + n2 = -4n + 4n Combine like terms: -4n + 4n = 0 -13 + 4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 4n + 13 + n2 = 0 + 13 Reorder the terms: -13 + 13 + 4n + n2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 4n + n2 = 0 + 13 4n + n2 = 0 + 13 Combine like terms: 0 + 13 = 13 4n + n2 = 13 The n term is 4n. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4n + 4 + n2 = 13 + 4 Reorder the terms: 4 + 4n + n2 = 13 + 4 Combine like terms: 13 + 4 = 17 4 + 4n + n2 = 17 Factor a perfect square on the left side: (n + 2)(n + 2) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (n + 2) equal to 4.123105626 and -4.123105626.Subproblem 1
n + 2 = 4.123105626 Simplifying n + 2 = 4.123105626 Reorder the terms: 2 + n = 4.123105626 Solving 2 + n = 4.123105626 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 4.123105626 + -2 Combine like terms: 2 + -2 = 0 0 + n = 4.123105626 + -2 n = 4.123105626 + -2 Combine like terms: 4.123105626 + -2 = 2.123105626 n = 2.123105626 Simplifying n = 2.123105626Subproblem 2
n + 2 = -4.123105626 Simplifying n + 2 = -4.123105626 Reorder the terms: 2 + n = -4.123105626 Solving 2 + n = -4.123105626 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = -4.123105626 + -2 Combine like terms: 2 + -2 = 0 0 + n = -4.123105626 + -2 n = -4.123105626 + -2 Combine like terms: -4.123105626 + -2 = -6.123105626 n = -6.123105626 Simplifying n = -6.123105626Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.123105626, -6.123105626}
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