y^2-12y+6=0

Simple and best practice solution for y^2-12y+6=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+6=0 equation:


Simplifying
y2 + -12y + 6 = 0

Reorder the terms:
6 + -12y + y2 = 0

Solving
6 + -12y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -12y + -6 + y2 = 0 + -6

Reorder the terms:
6 + -6 + -12y + y2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -12y + y2 = 0 + -6
-12y + y2 = 0 + -6

Combine like terms: 0 + -6 = -6
-12y + y2 = -6

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 = -6 + 36

Reorder the terms:
36 + -12y + y2 = -6 + 36

Combine like terms: -6 + 36 = 30
36 + -12y + y2 = 30

Factor a perfect square on the left side:
(y + -6)(y + -6) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(y + -6) equal to 5.477225575 and -5.477225575.

Subproblem 1

y + -6 = 5.477225575 Simplifying y + -6 = 5.477225575 Reorder the terms: -6 + y = 5.477225575 Solving -6 + y = 5.477225575 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 = 5.477225575 + 6 Combine like terms: -6 + 6 = 0 0 + y = 5.477225575 + 6 y = 5.477225575 + 6 Combine like terms: 5.477225575 + 6 = 11.477225575 y = 11.477225575 Simplifying y = 11.477225575

Subproblem 2

y + -6 = -5.477225575 Simplifying y + -6 = -5.477225575 Reorder the terms: -6 + y = -5.477225575 Solving -6 + y = -5.477225575 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 = -5.477225575 + 6 Combine like terms: -6 + 6 = 0 0 + y = -5.477225575 + 6 y = -5.477225575 + 6 Combine like terms: -5.477225575 + 6 = 0.522774425 y = 0.522774425 Simplifying y = 0.522774425

Solution

The solution to the problem is based on the solutions from the subproblems. y = {11.477225575, 0.522774425}

See similar equations:

| 26+x=9 | | 12a+3=24d | | c-29=2c-77 | | x^2+xy+y^2-3=0 | | x*19=y | | 3x+7=-25-5x | | 2a-34=a-17 | | x+8x+1=100 | | 25=4x-11 | | 28=x+17 | | 7+9+7r=4(3+2r)-3 | | 1/5z-1/3(4z)= | | 2y-50=y-19 | | 8x^2+5x-12=0 | | y=20x^2-27x-8 | | 11=n-66 | | c+4=8c-73 | | 3a=24z | | 6x^2+2=7x-7x | | log^5(x+30)=3 | | X-20=65 | | 26-6y=15 | | y^2-4y-45= | | -12=0x+3 | | 8w-65=3w | | 18x=6x^2+27 | | y^2-4y-44= | | 6.75(57n+94)=6.75(-3n-98) | | 2.3x+13.17=1.3x+2.9 | | 2(x-10)=2x-20 | | 12x+14=22+10x | | 5/4w=20 |

Equations solver categories