y^2-12y-243=0

Simple and best practice solution for y^2-12y-243=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-243=0 equation:


Simplifying
y2 + -12y + -243 = 0

Reorder the terms:
-243 + -12y + y2 = 0

Solving
-243 + -12y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '243' to each side of the equation.
-243 + -12y + 243 + y2 = 0 + 243

Reorder the terms:
-243 + 243 + -12y + y2 = 0 + 243

Combine like terms: -243 + 243 = 0
0 + -12y + y2 = 0 + 243
-12y + y2 = 0 + 243

Combine like terms: 0 + 243 = 243
-12y + y2 = 243

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 = 243 + 36

Reorder the terms:
36 + -12y + y2 = 243 + 36

Combine like terms: 243 + 36 = 279
36 + -12y + y2 = 279

Factor a perfect square on the left side:
(y + -6)(y + -6) = 279

Calculate the square root of the right side: 16.703293088

Break this problem into two subproblems by setting 
(y + -6) equal to 16.703293088 and -16.703293088.

Subproblem 1

y + -6 = 16.703293088 Simplifying y + -6 = 16.703293088 Reorder the terms: -6 + y = 16.703293088 Solving -6 + y = 16.703293088 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 = 16.703293088 + 6 Combine like terms: -6 + 6 = 0 0 + y = 16.703293088 + 6 y = 16.703293088 + 6 Combine like terms: 16.703293088 + 6 = 22.703293088 y = 22.703293088 Simplifying y = 22.703293088

Subproblem 2

y + -6 = -16.703293088 Simplifying y + -6 = -16.703293088 Reorder the terms: -6 + y = -16.703293088 Solving -6 + y = -16.703293088 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 = -16.703293088 + 6 Combine like terms: -6 + 6 = 0 0 + y = -16.703293088 + 6 y = -16.703293088 + 6 Combine like terms: -16.703293088 + 6 = -10.703293088 y = -10.703293088 Simplifying y = -10.703293088

Solution

The solution to the problem is based on the solutions from the subproblems. y = {22.703293088, -10.703293088}

See similar equations:

| 9(i-3)=-3(2i+4) | | 3(2z+25)=78+2(z-1) | | Xx(x+4)=77 | | 3(2z+25)=78 | | (-3x+6)-(2x-8)= | | n+4(n)+5(n)=50 | | f(x)=sin(x) | | 6x^2-2r=0 | | 11x+8+9=105 | | ln(e)+X=25 | | 3-(2x-3)=-6 | | (256)1/8 | | 8y-4=7y-2 | | 17-3=5 | | (4/3)*pi*(r^X) | | 4(x-1)+2=4x | | (x-3)(x+3)=x(x-2)+x(x-3) | | 5x^(2/5)*(-x^(3/5)) | | 3+(t+9)=15 | | 5x-3+6x=11x-3 | | 11x+8+9=180 | | C(x)=1.5x^2-144x+5853 | | -9=-x/3 | | X+(X+21)=169 | | 7x+1=7x-3 | | 16x^2-28x+7=0 | | 5(x+3)+7x=39 | | (n)4(n)5(n)=50 | | 5.25+2y=5 | | F(x)=8x^3-6 | | 3(u-3)-7u=-1 | | Lg(x)=69-2*lg(10) |

Equations solver categories