9y^2-30y=25

Simple and best practice solution for 9y^2-30y=25 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 9y^2-30y=25 equation: 


Simplifying
9y2 + -30y = 25

Reorder the terms:
-30y + 9y2 = 25

Solving
-30y + 9y2 = 25

Solving for variable 'y'.

Reorder the terms:
-25 + -30y + 9y2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + -30y + 9y2 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-2.777777778 + -3.333333333y + y2 = 0

Move the constant term to the right:

Add '2.777777778' to each side of the equation.
-2.777777778 + -3.333333333y + 2.777777778 + y2 = 0 + 2.777777778

Reorder the terms:
-2.777777778 + 2.777777778 + -3.333333333y + y2 = 0 + 2.777777778

Combine like terms: -2.777777778 + 2.777777778 = 0.000000000
0.000000000 + -3.333333333y + y2 = 0 + 2.777777778
-3.333333333y + y2 = 0 + 2.777777778

Combine like terms: 0 + 2.777777778 = 2.777777778
-3.333333333y + y2 = 2.777777778

The y term is -3.333333333y.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333y + 2.777777779 + y2 = 2.777777778 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333y + y2 = 2.777777778 + 2.777777779

Combine like terms: 2.777777778 + 2.777777779 = 5.555555557
2.777777779 + -3.333333333y + y2 = 5.555555557

Factor a perfect square on the left side:
(y + -1.666666667)(y + -1.666666667) = 5.555555557

Calculate the square root of the right side: 2.357022604

Break this problem into two subproblems by setting 
(y + -1.666666667) equal to 2.357022604 and -2.357022604.


Subproblem 1
y + -1.666666667 = 2.357022604

Simplifying
y + -1.666666667 = 2.357022604

Reorder the terms:
-1.666666667 + y = 2.357022604

Solving
-1.666666667 + y = 2.357022604

Solving for variable 'y'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + y = 2.357022604 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + y = 2.357022604 + 1.666666667
y = 2.357022604 + 1.666666667

Combine like terms: 2.357022604 + 1.666666667 = 4.023689271
y = 4.023689271

Simplifying
y = 4.023689271


Subproblem 2
y + -1.666666667 = -2.357022604

Simplifying
y + -1.666666667 = -2.357022604

Reorder the terms:
-1.666666667 + y = -2.357022604

Solving
-1.666666667 + y = -2.357022604

Solving for variable 'y'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + y = -2.357022604 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + y = -2.357022604 + 1.666666667
y = -2.357022604 + 1.666666667

Combine like terms: -2.357022604 + 1.666666667 = -0.690355937
y = -0.690355937

Simplifying
y = -0.690355937


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.023689271, -0.690355937}

See similar equations:

| 500/10,000=p/100 | | -6/7b=12 | | 3(4x+5)=-40+31 | | 9/10v=-18 | | 15/16c=30 | | -2/5x=-20 | | -9/10g=18 | | -3/5d=24 | | 8/16s=-8 | | 20b+1-6b-1= | | 5y+1+3y= | | 5/8r=25 | | 4b*5+1-6b+1= | | 4*0+5y=20 | | 2x^2=45-13x | | 6/10e=18 | | 3.8d=17.86 | | 13(13)= | | 4(5)+5y=20 | | 6+3(5+7)= | | 5/8y=20 | | 8/9p=16 | | 5/7m=5 | | 3/2x=21 | | n^2-2n-11=-3 | | x+(x/2+40)=352 | | 3/5g=9 | | (X-7)(x+19)=0 | | x+(x/2+40) | | 2/3f=6 | | 5b^2+6b-8=0 | | 4z+4z=7z-3 |

Equations solver categories