n^2+4n-13=0

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Solution for n^2+4n-13=0 equation:


Simplifying
n2 + 4n + -13 = 0

Reorder the terms:
-13 + 4n + n2 = 0

Solving
-13 + 4n + n2 = 0

Solving for variable 'n'.

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 = 2.123105626

Subproblem 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 = -6.123105626

Solution

The solution to the problem is based on the solutions from the subproblems. n = {2.123105626, -6.123105626}

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