y^2=6y+9

Simple and best practice solution for y^2=6y+9 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=6y+9 equation:


Simplifying
y2 = 6y + 9

Reorder the terms:
y2 = 9 + 6y

Solving
y2 = 9 + 6y

Solving for variable 'y'.

Reorder the terms:
-9 + -6y + y2 = 9 + 6y + -9 + -6y

Reorder the terms:
-9 + -6y + y2 = 9 + -9 + 6y + -6y

Combine like terms: 9 + -9 = 0
-9 + -6y + y2 = 0 + 6y + -6y
-9 + -6y + y2 = 6y + -6y

Combine like terms: 6y + -6y = 0
-9 + -6y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -6y + 9 + y2 = 0 + 9

Reorder the terms:
-9 + 9 + -6y + y2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -6y + y2 = 0 + 9
-6y + y2 = 0 + 9

Combine like terms: 0 + 9 = 9
-6y + y2 = 9

The y term is -6y.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6y + 9 + y2 = 9 + 9

Reorder the terms:
9 + -6y + y2 = 9 + 9

Combine like terms: 9 + 9 = 18
9 + -6y + y2 = 18

Factor a perfect square on the left side:
(y + -3)(y + -3) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(y + -3) equal to 4.242640687 and -4.242640687.

Subproblem 1

y + -3 = 4.242640687 Simplifying y + -3 = 4.242640687 Reorder the terms: -3 + y = 4.242640687 Solving -3 + y = 4.242640687 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + y = 4.242640687 + 3 y = 4.242640687 + 3 Combine like terms: 4.242640687 + 3 = 7.242640687 y = 7.242640687 Simplifying y = 7.242640687

Subproblem 2

y + -3 = -4.242640687 Simplifying y + -3 = -4.242640687 Reorder the terms: -3 + y = -4.242640687 Solving -3 + y = -4.242640687 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + y = -4.242640687 + 3 y = -4.242640687 + 3 Combine like terms: -4.242640687 + 3 = -1.242640687 y = -1.242640687 Simplifying y = -1.242640687

Solution

The solution to the problem is based on the solutions from the subproblems. y = {7.242640687, -1.242640687}

See similar equations:

| 2+4lnx=11 | | 2n-7=n-10 | | tn=4n-2 | | 4x^2*x^(1/2) | | 17c+4=15c+40 | | 6x^2-18x-24=75 | | 5n-7=-13 | | .09/100 | | 1992/873.36-2.15 | | x+x+1+x+2=69 | | -6c-4-5c=10+18 | | x^2+(170.868*x)-123024.96=0 | | 8-(4x+6)=29-7x | | x+3(0)=-1 | | y=16+4x | | 7n=6n+3 | | -3(4x+3)=43+6x-1 | | 2(2a+3)=4(a+1) | | 2(6+4x)=5(2x+4) | | 2(6x+4)=5(2x+4) | | y=-35x+1500 | | -9x-21=35-5x | | -9x+5x+18-8x= | | 2x=4i | | -9x+5+18-8x= | | 9x+3=-5+5x+20 | | 4ln(2x+7)=12 | | T=1+5n | | (x+1)dy=5x^2(x+1)dx-y | | 13(4x+2)=18(10x+7)+9(6x*1) | | 2(2f-1)+3(4-2f)=2(f+1)+2(f+6) | | y-0.6y+240= |

Equations solver categories