n^2-6n-13=0

Simple and best practice solution for n^2-6n-13=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

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 = 7.69041576 n = 7.69041576 Simplifying n = 7.69041576

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 = -1.69041576 n = -1.69041576 Simplifying n = -1.69041576

Solution

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

See similar equations:

| X+x+55+x+38=180 | | 40d+55=695 | | 9x+1=6x-14 | | (22+2x)(16+2x)=1080 | | 6y=9y+12 | | V^2-2v+1=4 | | -5-7(2p-4)=93 | | (b-66)4=a | | 3x=4x+4+5x-3+17 | | -2(-7b+8)=-128 | | 22x-3.6=20x | | 2r^3+7r^2+5R= | | 5.4q-5.8-5.9q=-1.5q-3.9 | | -7+x=3x+3 | | 5(5y-x)=12-8Y | | 6+3v= | | x^2+14x+143=0 | | X+15+3x+x=180 | | 4+6x^2-19x= | | 18x+9=9x+50 | | 1.2x=5.16 | | -4(5b+7)=4-4b | | -1(r^2-7r+8)=0 | | -2x-8=x+7 | | 22x-36=20x | | 18-7n+1=34 | | 5x+4y=12+3solvey | | 8=12c+5 | | 4t+4y-8= | | 8(2t+1)(t-7)=0 | | -7(-5v-1)=7+3v | | (x+3)+4=400 |

Equations solver categories