3y^2+7y+3=

Simple and best practice solution for 3y^2+7y+3= 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+7y+3= equation:


Simplifying
3y2 + 7y + 3 = 0

Reorder the terms:
3 + 7y + 3y2 = 0

Solving
3 + 7y + 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'.
1 + 2.333333333y + y2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 2.333333333y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + 2.333333333y + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2.333333333y + y2 = 0 + -1
2.333333333y + y2 = 0 + -1

Combine like terms: 0 + -1 = -1
2.333333333y + y2 = -1

The y term is 2.333333333y.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333y + 1.361111112 + y2 = -1 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333y + y2 = -1 + 1.361111112

Combine like terms: -1 + 1.361111112 = 0.361111112
1.361111112 + 2.333333333y + y2 = 0.361111112

Factor a perfect square on the left side:
(y + 1.166666667)(y + 1.166666667) = 0.361111112

Calculate the square root of the right side: 0.600925213

Break this problem into two subproblems by setting 
(y + 1.166666667) equal to 0.600925213 and -0.600925213.

Subproblem 1

y + 1.166666667 = 0.600925213 Simplifying y + 1.166666667 = 0.600925213 Reorder the terms: 1.166666667 + y = 0.600925213 Solving 1.166666667 + y = 0.600925213 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + y = 0.600925213 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + y = 0.600925213 + -1.166666667 y = 0.600925213 + -1.166666667 Combine like terms: 0.600925213 + -1.166666667 = -0.565741454 y = -0.565741454 Simplifying y = -0.565741454

Subproblem 2

y + 1.166666667 = -0.600925213 Simplifying y + 1.166666667 = -0.600925213 Reorder the terms: 1.166666667 + y = -0.600925213 Solving 1.166666667 + y = -0.600925213 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + y = -0.600925213 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + y = -0.600925213 + -1.166666667 y = -0.600925213 + -1.166666667 Combine like terms: -0.600925213 + -1.166666667 = -1.76759188 y = -1.76759188 Simplifying y = -1.76759188

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-0.565741454, -1.76759188}

See similar equations:

| 9x+13/x+4 | | -6(2p-8)=p-30 | | -5(a+7)=70 | | 3n+3=-2n-8 | | 21=9k-6 | | 7x+2=2(46-x) | | 5x+7=83-3x | | t+-65=162 | | -(31-k)+24=-5 | | -6(1-7p)-2(p-3)=6p-6p | | 56=3v+11 | | 1.5/5=6.75/n | | 3x+4=9+(6x+1) | | -26=4-3X | | B/b-9=10/3 | | w+928=855 | | 13=6j-11 | | 4(2x-5)/3=-20 | | 6x+4=9+(6x+1) | | g+284=-270 | | lx-3l=4 | | 1/4(4+k)=25 | | 6y-9=y+8 | | 5*1/5*z=5*20/3 | | 3x=5x-112 | | 999999999999999999999*1000=a | | c+268=501 | | 4x+4+92=180 | | 4p-3=9p-2 | | 57467575*484848=a | | 12x-30=42 | | 2y-9y+13+y=-23 |

Equations solver categories