4y^2-24y+9=

Simple and best practice solution for 4y^2-24y+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 4y^2-24y+9= equation:


Simplifying
4y2 + -24y + 9 = 0

Reorder the terms:
9 + -24y + 4y2 = 0

Solving
9 + -24y + 4y2 = 0

Solving for variable 'y'.

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

Divide each side by '4'.
2.25 + -6y + y2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -6y + -2.25 + y2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + -6y + y2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -6y + y2 = 0 + -2.25
-6y + y2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
-6y + y2 = -2.25

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 = -2.25 + 9

Reorder the terms:
9 + -6y + y2 = -2.25 + 9

Combine like terms: -2.25 + 9 = 6.75
9 + -6y + y2 = 6.75

Factor a perfect square on the left side:
(y + -3)(y + -3) = 6.75

Calculate the square root of the right side: 2.598076211

Break this problem into two subproblems by setting 
(y + -3) equal to 2.598076211 and -2.598076211.

Subproblem 1

y + -3 = 2.598076211 Simplifying y + -3 = 2.598076211 Reorder the terms: -3 + y = 2.598076211 Solving -3 + y = 2.598076211 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 = 2.598076211 + 3 Combine like terms: -3 + 3 = 0 0 + y = 2.598076211 + 3 y = 2.598076211 + 3 Combine like terms: 2.598076211 + 3 = 5.598076211 y = 5.598076211 Simplifying y = 5.598076211

Subproblem 2

y + -3 = -2.598076211 Simplifying y + -3 = -2.598076211 Reorder the terms: -3 + y = -2.598076211 Solving -3 + y = -2.598076211 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 = -2.598076211 + 3 Combine like terms: -3 + 3 = 0 0 + y = -2.598076211 + 3 y = -2.598076211 + 3 Combine like terms: -2.598076211 + 3 = 0.401923789 y = 0.401923789 Simplifying y = 0.401923789

Solution

The solution to the problem is based on the solutions from the subproblems. y = {5.598076211, 0.401923789}

See similar equations:

| 16xy-18+7xy= | | 3y^2+7y-6= | | 2x/3-2/3-x/5+2/5-x/3-2/3 | | 41m-8=8 | | 2d+10=16-10 | | 4(m-8)=8 | | 5r-7r+8m= | | x-.14(x)=495.00 | | -x+3x=-x+7x+24+40 | | 2x^2-4x=5 | | 4m-8=4 | | x+4/9=10 | | 9a-6a+3b= | | x-.14(x)=520 | | 25+30x=65+20x | | 5p/p-6 | | lny=8lnx | | (6w3-8w2+2w)/2w | | -3x+5+x=-15 | | x^2-5/4x+25/64=121/64 | | -7+2(-6x-2)=-137 | | 30+0.05m=49.75 | | 8w-12=-12 | | 12=-x | | 10-3x=-3 | | -16x^2+18x+10=0 | | h-h/4+1/4-2h/5-3/5-1 | | 7.5+2.5x=12.5 | | 3x=-2x+4x-24 | | 1/(x-1)+2/(x+1)=6/(x^2-1) | | 4m-8=8 | | -5.5+6.5(1-3s)=-21.5 |

Equations solver categories