n^2-4n-25=0

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Solution for n^2-4n-25=0 equation:


Simplifying
n2 + -4n + -25 = 0

Reorder the terms:
-25 + -4n + n2 = 0

Solving
-25 + -4n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -4n + 25 + n2 = 0 + 25

Reorder the terms:
-25 + 25 + -4n + n2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -4n + n2 = 0 + 25
-4n + n2 = 0 + 25

Combine like terms: 0 + 25 = 25
-4n + n2 = 25

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 = 25 + 4

Reorder the terms:
4 + -4n + n2 = 25 + 4

Combine like terms: 25 + 4 = 29
4 + -4n + n2 = 29

Factor a perfect square on the left side:
(n + -2)(n + -2) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(n + -2) equal to 5.385164807 and -5.385164807.

Subproblem 1

n + -2 = 5.385164807 Simplifying n + -2 = 5.385164807 Reorder the terms: -2 + n = 5.385164807 Solving -2 + n = 5.385164807 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 = 5.385164807 + 2 Combine like terms: -2 + 2 = 0 0 + n = 5.385164807 + 2 n = 5.385164807 + 2 Combine like terms: 5.385164807 + 2 = 7.385164807 n = 7.385164807 Simplifying n = 7.385164807

Subproblem 2

n + -2 = -5.385164807 Simplifying n + -2 = -5.385164807 Reorder the terms: -2 + n = -5.385164807 Solving -2 + n = -5.385164807 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 = -5.385164807 + 2 Combine like terms: -2 + 2 = 0 0 + n = -5.385164807 + 2 n = -5.385164807 + 2 Combine like terms: -5.385164807 + 2 = -3.385164807 n = -3.385164807 Simplifying n = -3.385164807

Solution

The solution to the problem is based on the solutions from the subproblems. n = {7.385164807, -3.385164807}

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