9y^2-30y+23=0

Simple and best practice solution for 9y^2-30y+23=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 9y^2-30y+23=0 equation:


Simplifying
9y2 + -30y + 23 = 0

Reorder the terms:
23 + -30y + 9y2 = 0

Solving
23 + -30y + 9y2 = 0

Solving for variable 'y'.

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

Divide each side by '9'.
2.555555556 + -3.333333333y + y2 = 0

Move the constant term to the right:

Add '-2.555555556' to each side of the equation.
2.555555556 + -3.333333333y + -2.555555556 + y2 = 0 + -2.555555556

Reorder the terms:
2.555555556 + -2.555555556 + -3.333333333y + y2 = 0 + -2.555555556

Combine like terms: 2.555555556 + -2.555555556 = 0.000000000
0.000000000 + -3.333333333y + y2 = 0 + -2.555555556
-3.333333333y + y2 = 0 + -2.555555556

Combine like terms: 0 + -2.555555556 = -2.555555556
-3.333333333y + y2 = -2.555555556

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 = -2.555555556 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333y + y2 = -2.555555556 + 2.777777779

Combine like terms: -2.555555556 + 2.777777779 = 0.222222223
2.777777779 + -3.333333333y + y2 = 0.222222223

Factor a perfect square on the left side:
(y + -1.666666667)(y + -1.666666667) = 0.222222223

Calculate the square root of the right side: 0.471404522

Break this problem into two subproblems by setting 
(y + -1.666666667) equal to 0.471404522 and -0.471404522.

Subproblem 1

y + -1.666666667 = 0.471404522 Simplifying y + -1.666666667 = 0.471404522 Reorder the terms: -1.666666667 + y = 0.471404522 Solving -1.666666667 + y = 0.471404522 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 = 0.471404522 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + y = 0.471404522 + 1.666666667 y = 0.471404522 + 1.666666667 Combine like terms: 0.471404522 + 1.666666667 = 2.138071189 y = 2.138071189 Simplifying y = 2.138071189

Subproblem 2

y + -1.666666667 = -0.471404522 Simplifying y + -1.666666667 = -0.471404522 Reorder the terms: -1.666666667 + y = -0.471404522 Solving -1.666666667 + y = -0.471404522 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 = -0.471404522 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + y = -0.471404522 + 1.666666667 y = -0.471404522 + 1.666666667 Combine like terms: -0.471404522 + 1.666666667 = 1.195262145 y = 1.195262145 Simplifying y = 1.195262145

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.138071189, 1.195262145}

See similar equations:

| 106-4x=3x | | x^2-xy=0 | | 7x-8=48 | | b+7+2b+10= | | 7x+11=32 | | 2x^2-24x-34= | | y=-2x^2-20x-48 | | 130-4x=41x+15 | | 89-5x=22x+20 | | x=2*x-2 | | 4(17x-6)+2=2(8x-16)-13 | | 2c-4=25 | | 2c-24=5 | | 11+9=8x+21 | | 6x^2-8x+2=0 | | -6=B-18 | | ln(2x-1)+ln(2x+1)-2ln(x-2)=2 | | (2a-b)-(2a-6b)= | | 128-6x=3x+20 | | 94-5x=22x+16 | | f=123-6t | | 2a-b= | | 9n-27=45 | | 152-5x=6x+9 | | 6*6+x=40 | | x+2=38 | | 13x+8-2x=24+2x-28 | | 13x+4(x+1)=17(x+1)-13 | | t^2-4t-12=0 | | 6x-48+4=7+3x | | (3x^2-2)(x^2+4)=0 | | 4x^2-24x+37=0 |

Equations solver categories