2y^2+9y=4

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


Simplifying
2y2 + 9y = 4

Reorder the terms:
9y + 2y2 = 4

Solving
9y + 2y2 = 4

Solving for variable 'y'.

Reorder the terms:
-4 + 9y + 2y2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 9y + 2y2 = 0

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

Divide each side by '2'.
-2 + 4.5y + y2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 4.5y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + 4.5y + y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 4.5y + y2 = 0 + 2
4.5y + y2 = 0 + 2

Combine like terms: 0 + 2 = 2
4.5y + y2 = 2

The y term is 4.5y.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5y + 5.0625 + y2 = 2 + 5.0625

Reorder the terms:
5.0625 + 4.5y + y2 = 2 + 5.0625

Combine like terms: 2 + 5.0625 = 7.0625
5.0625 + 4.5y + y2 = 7.0625

Factor a perfect square on the left side:
(y + 2.25)(y + 2.25) = 7.0625

Calculate the square root of the right side: 2.657536453

Break this problem into two subproblems by setting 
(y + 2.25) equal to 2.657536453 and -2.657536453.

Subproblem 1

y + 2.25 = 2.657536453 Simplifying y + 2.25 = 2.657536453 Reorder the terms: 2.25 + y = 2.657536453 Solving 2.25 + y = 2.657536453 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + y = 2.657536453 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + y = 2.657536453 + -2.25 y = 2.657536453 + -2.25 Combine like terms: 2.657536453 + -2.25 = 0.407536453 y = 0.407536453 Simplifying y = 0.407536453

Subproblem 2

y + 2.25 = -2.657536453 Simplifying y + 2.25 = -2.657536453 Reorder the terms: 2.25 + y = -2.657536453 Solving 2.25 + y = -2.657536453 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + y = -2.657536453 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + y = -2.657536453 + -2.25 y = -2.657536453 + -2.25 Combine like terms: -2.657536453 + -2.25 = -4.907536453 y = -4.907536453 Simplifying y = -4.907536453

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.407536453, -4.907536453}

See similar equations:

| 16x-8x=40 | | 174=95-x | | 16/24=x/18 | | 27=-x+232 | | 17x/16=7 | | 65+x=93 | | 21=-7(x-5) | | 0=16t^2+13t-13 | | 3(x+8)=2(4x+22) | | 3t^2-2/3=2 | | 3+.5(4a+8)=9-2a | | h/8-11=26 | | 48-u=5u | | 2n^2-4=1/2 | | (X+7)(X+7)=11 | | 2x-10=7x-qw | | 9x=.5(12x-2) | | 198-w=266 | | 12u=9u+6 | | 3*X*X=9 | | 14y=16 | | 236-y=113 | | 3a-7=-12 | | 4x+(-12)=42 | | 23-2q/3=17 | | 289=-w+118 | | X^2+16x+y^2-12y=44 | | 8w=2720 | | -2[x+7]=28 | | -5x-4/7=-1 | | 29-29/3=17 | | X(x+2)=50 |

Equations solver categories