y^2-12y-36=0

Simple and best practice solution for y^2-12y-36=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 y^2-12y-36=0 equation: 


Simplifying
y2 + -12y + -36 = 0

Reorder the terms:
-36 + -12y + y2 = 0

Solving
-36 + -12y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -12y + 36 + y2 = 0 + 36

Reorder the terms:
-36 + 36 + -12y + y2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -12y + y2 = 0 + 36
-12y + y2 = 0 + 36

Combine like terms: 0 + 36 = 36
-12y + y2 = 36

The y term is -12y.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12y + 36 + y2 = 36 + 36

Reorder the terms:
36 + -12y + y2 = 36 + 36

Combine like terms: 36 + 36 = 72
36 + -12y + y2 = 72

Factor a perfect square on the left side:
(y + -6)(y + -6) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(y + -6) equal to 8.485281374 and -8.485281374.


Subproblem 1
y + -6 = 8.485281374

Simplifying
y + -6 = 8.485281374

Reorder the terms:
-6 + y = 8.485281374

Solving
-6 + y = 8.485281374

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + y = 8.485281374 + 6

Combine like terms: -6 + 6 = 0
0 + y = 8.485281374 + 6
y = 8.485281374 + 6

Combine like terms: 8.485281374 + 6 = 14.485281374
y = 14.485281374

Simplifying
y = 14.485281374


Subproblem 2
y + -6 = -8.485281374

Simplifying
y + -6 = -8.485281374

Reorder the terms:
-6 + y = -8.485281374

Solving
-6 + y = -8.485281374

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + y = -8.485281374 + 6

Combine like terms: -6 + 6 = 0
0 + y = -8.485281374 + 6
y = -8.485281374 + 6

Combine like terms: -8.485281374 + 6 = -2.485281374
y = -2.485281374

Simplifying
y = -2.485281374


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {14.485281374, -2.485281374}

See similar equations:

| -1.25x=2+8 | | 8x+1=27x+4 | | 4x^2-x+5=x+9 | | -1.25x=8-2 | | 6(2n+2)=6(6n+3)+2 | | (4x^2)-x+5=x+9 | | -1.25x=8-6 | | -3/8y=3/16-9/16 | | -5y-9=21 | | 6(y-1)-(2y)=6 | | I/6-k=5 | | -3(t-4)+5t=4t-4 | | 2-x+-2=8 | | -.03x=400-700 | | 5b+2=c | | -.3x=400-700 | | 3n+5=25 | | -300x=400-700 | | 7x+8=3x+36 | | 8/v=3/6 | | -30x=700-400 | | 7v^2+35-42=0 | | 30=-3(a-7) | | 6=5(a-7) | | 15x+4000=10x+10000 | | -b-4(1+7b)=228 | | 0.1x^2+5x-140=0 | | 12t(t+2)=t-10 | | -30x=400-700 | | c=450m+75 | | 15x-4000=10x+10000 | | 12t^2+24t+10=0 |

Equations solver categories