3y^2+y-18=0

Simple and best practice solution for 3y^2+y-18=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 3y^2+y-18=0 equation:


Simplifying
3y2 + y + -18 = 0

Reorder the terms:
-18 + y + 3y2 = 0

Solving
-18 + y + 3y2 = 0

Solving for variable 'y'.

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

Divide each side by '3'.
-6 + 0.3333333333y + y2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 0.3333333333y + 6 + y2 = 0 + 6

Reorder the terms:
-6 + 6 + 0.3333333333y + y2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 0.3333333333y + y2 = 0 + 6
0.3333333333y + y2 = 0 + 6

Combine like terms: 0 + 6 = 6
0.3333333333y + y2 = 6

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.3333333333y + 0.25 + y2 = 6 + 0.25

Reorder the terms:
0.25 + 0.3333333333y + y2 = 6 + 0.25

Combine like terms: 6 + 0.25 = 6.25
0.25 + 0.3333333333y + y2 = 6.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 6.25

Calculate the square root of the right side: 2.5

Break this problem into two subproblems by setting 
(y + 0.5) equal to 2.5 and -2.5.

Subproblem 1

y + 0.5 = 2.5 Simplifying y + 0.5 = 2.5 Reorder the terms: 0.5 + y = 2.5 Solving 0.5 + y = 2.5 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 2.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 2.5 + -0.5 y = 2.5 + -0.5 Combine like terms: 2.5 + -0.5 = 2 y = 2 Simplifying y = 2

Subproblem 2

y + 0.5 = -2.5 Simplifying y + 0.5 = -2.5 Reorder the terms: 0.5 + y = -2.5 Solving 0.5 + y = -2.5 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -2.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -2.5 + -0.5 y = -2.5 + -0.5 Combine like terms: -2.5 + -0.5 = -3 y = -3 Simplifying y = -3

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2, -3}

See similar equations:

| -7(2b+3)+(15b-6)=0 | | 9y=12-3.947368421 | | 4x^3-10x^2+2x-5=0 | | -6x+6y=30 | | 2x^2+2y^2+2x+2y=11 | | -6x+6x=30 | | 17d+29=-1+2d | | 63x^3-35x^2+18x-10=0 | | r^2-12tw+4wr-3tr=0 | | 6x^2=x^2+1 | | 5x+17=9x-3 | | 8(x+7)=7+7x | | 16x^3-12x^2+4x=0 | | 3a^2g^2-12ag= | | -8z+10=4 | | (4m^2-6)(4m^2-6)=81 | | 4.9q-1.5-4.9q=-1.4q-3.3 | | 3r^2-19r=14 | | -8x^5-4x^4=0 | | 3t-13=2t+14 | | 3=9-3 | | -3y+8=-4y+4 | | 15-h=19 | | 42=3(x^2+5) | | 9x^2+x-6=0 | | 6(y+9)=5y-3 | | 1.3(k-6)(k-6)=20 | | 0.5(c-8)(c-8)=3 | | -X^2+7X=10 | | m+-15=30 | | 5y-9+y+21=6y+20-4y | | (6t-3)=2(t+1)+2 |

Equations solver categories