n^2-6n=13

Simple and best practice solution for n^2-6n=13 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 equation:


Simplifying
n2 + -6n = 13

Reorder the terms:
-6n + n2 = 13

Solving
-6n + n2 = 13

Solving for variable 'n'.

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

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

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:

| d=1/2(4)(2)^2+3(2) | | 5x+8=8x+9 | | n^2-2n-7=0 | | 2-16=z/-7 | | 4m^2-12m=0 | | 3(g+7)+2=6g-2+2g | | 152=73.502+3.876h | | y=-3(1.5)+8 | | x/2=-3-(-6) | | 4x^2=16x+13 | | x-(-3x+8)=-2 | | .05x+.12x(x+5000)=940 | | 4t+2=5(t+10) | | 152=64.977+3.144h | | P=5n+5z | | x^2/10-x/5+2=0 | | 2y^2-4y-8=-1y^2+1y | | x=5(3)-4 | | 4/3x=1/2 | | 152=72.572+2.533t | | x-8/5+8/5=-x/3 | | 5x+7=-x+3 | | 4(2x-1)=27-3(2x-5) | | 4p+5q=53 | | 3(5y-4)+2y=39 | | 2p-4(-2p+1)= | | x+0.08(20)=0.2(20+x) | | 5x=mx+y | | 5r-1-4r=r+7 | | 5p^2-25=4p^2+25 | | 8x-12-3a=9x-7 | | 19x+31+93-5x=180 |

Equations solver categories