y^2+23=12y

Simple and best practice solution for y^2+23=12y 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+23=12y equation:


Simplifying
y2 + 23 = 12y

Reorder the terms:
23 + y2 = 12y

Solving
23 + y2 = 12y

Solving for variable 'y'.

Reorder the terms:
23 + -12y + y2 = 12y + -12y

Combine like terms: 12y + -12y = 0
23 + -12y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-23' to each side of the equation.
23 + -12y + -23 + y2 = 0 + -23

Reorder the terms:
23 + -23 + -12y + y2 = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -12y + y2 = 0 + -23
-12y + y2 = 0 + -23

Combine like terms: 0 + -23 = -23
-12y + y2 = -23

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 = -23 + 36

Reorder the terms:
36 + -12y + y2 = -23 + 36

Combine like terms: -23 + 36 = 13
36 + -12y + y2 = 13

Factor a perfect square on the left side:
(y + -6)(y + -6) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(y + -6) equal to 3.605551275 and -3.605551275.

Subproblem 1

y + -6 = 3.605551275 Simplifying y + -6 = 3.605551275 Reorder the terms: -6 + y = 3.605551275 Solving -6 + y = 3.605551275 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 = 3.605551275 + 6 Combine like terms: -6 + 6 = 0 0 + y = 3.605551275 + 6 y = 3.605551275 + 6 Combine like terms: 3.605551275 + 6 = 9.605551275 y = 9.605551275 Simplifying y = 9.605551275

Subproblem 2

y + -6 = -3.605551275 Simplifying y + -6 = -3.605551275 Reorder the terms: -6 + y = -3.605551275 Solving -6 + y = -3.605551275 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 = -3.605551275 + 6 Combine like terms: -6 + 6 = 0 0 + y = -3.605551275 + 6 y = -3.605551275 + 6 Combine like terms: -3.605551275 + 6 = 2.394448725 y = 2.394448725 Simplifying y = 2.394448725

Solution

The solution to the problem is based on the solutions from the subproblems. y = {9.605551275, 2.394448725}

See similar equations:

| 7-X=19 | | 24x^2+22x-30= | | -6(3x+1)+(19x-2)=0 | | 11(v+1)-3v=2(4v+2)-8 | | x-5=3+4 | | z^6-3z^4-3z^2+2=0 | | z^6-3z^4-3z^2+2= | | 9x^2-72x-16y^2-32y-16=0 | | 3|3-x|=6 | | 8m-3=5m+12 | | 7p-8=13 | | a+5b=34 | | x+29.3+26.6=196.2 | | 3y+y=80 | | X^2-12x+20=-20 | | 6m(7n-4)+4(8mn-4m)= | | y^2-2y+2=0 | | 2x^2-8x+6+x-3=2x-2 | | 3p^2-5p+1=0 | | 3x+16+x=112 | | X^2-17+2=5 | | x^6-10x^2+5=0 | | (n+5)*3=n+31 | | 1-6(x-5)=10-6(x-9) | | x+4=x-4 | | x^2+3x+1=7x+22 | | -5(t-6)-(t-1)=7 | | 7(t-3)+7t=7(2t+2)-11 | | 9-5x=40 | | -2(5s-3)-6=-3(6s+-1)-5 | | 8y+7=-9y+3 | | (3x+4)(x-5)(x+1)=0 |

Equations solver categories