n^2+6n-13=0

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Solution for n^2+6n-13=0 equation:


Simplifying
n2 + 6n + -13 = 0

Reorder the terms:
-13 + 6n + n2 = 0

Solving
-13 + 6n + 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 + 6n + 13 + n2 = 0 + 13

Reorder the terms:
-13 + 13 + 6n + n2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 6n + n2 = 0 + 13
6n + n2 = 0 + 13

Combine like terms: 0 + 13 = 13
6n + n2 = 13

The n term is 6n.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6n + 9 + n2 = 13 + 9

Reorder the terms:
9 + 6n + n2 = 13 + 9

Combine like terms: 13 + 9 = 22
9 + 6n + n2 = 22

Factor a perfect square on the left side:
(n + 3)(n + 3) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(n + 3) equal to 4.69041576 and -4.69041576.

Subproblem 1

n + 3 = 4.69041576 Simplifying n + 3 = 4.69041576 Reorder the terms: 3 + n = 4.69041576 Solving 3 + n = 4.69041576 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = 4.69041576 + -3 Combine like terms: 3 + -3 = 0 0 + n = 4.69041576 + -3 n = 4.69041576 + -3 Combine like terms: 4.69041576 + -3 = 1.69041576 n = 1.69041576 Simplifying n = 1.69041576

Subproblem 2

n + 3 = -4.69041576 Simplifying n + 3 = -4.69041576 Reorder the terms: 3 + n = -4.69041576 Solving 3 + n = -4.69041576 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = -4.69041576 + -3 Combine like terms: 3 + -3 = 0 0 + n = -4.69041576 + -3 n = -4.69041576 + -3 Combine like terms: -4.69041576 + -3 = -7.69041576 n = -7.69041576 Simplifying n = -7.69041576

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.69041576, -7.69041576}

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