3x^2+16x+9=0

Simple and best practice solution for 3x^2+16x+9=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 3x^2+16x+9=0 equation: 


Simplifying
3x2 + 16x + 9 = 0

Reorder the terms:
9 + 16x + 3x2 = 0

Solving
9 + 16x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
3 + 5.333333333x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 5.333333333x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 5.333333333x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5.333333333x + x2 = 0 + -3
5.333333333x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
5.333333333x + x2 = -3

The x term is 5.333333333x.  Take half its coefficient (2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
5.333333333x + 7.111111113 + x2 = -3 + 7.111111113

Reorder the terms:
7.111111113 + 5.333333333x + x2 = -3 + 7.111111113

Combine like terms: -3 + 7.111111113 = 4.111111113
7.111111113 + 5.333333333x + x2 = 4.111111113

Factor a perfect square on the left side:
(x + 2.666666667)(x + 2.666666667) = 4.111111113

Calculate the square root of the right side: 2.027587511

Break this problem into two subproblems by setting 
(x + 2.666666667) equal to 2.027587511 and -2.027587511.


Subproblem 1
x + 2.666666667 = 2.027587511

Simplifying
x + 2.666666667 = 2.027587511

Reorder the terms:
2.666666667 + x = 2.027587511

Solving
2.666666667 + x = 2.027587511

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + x = 2.027587511 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + x = 2.027587511 + -2.666666667
x = 2.027587511 + -2.666666667

Combine like terms: 2.027587511 + -2.666666667 = -0.639079156
x = -0.639079156

Simplifying
x = -0.639079156


Subproblem 2
x + 2.666666667 = -2.027587511

Simplifying
x + 2.666666667 = -2.027587511

Reorder the terms:
2.666666667 + x = -2.027587511

Solving
2.666666667 + x = -2.027587511

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + x = -2.027587511 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + x = -2.027587511 + -2.666666667
x = -2.027587511 + -2.666666667

Combine like terms: -2.027587511 + -2.666666667 = -4.694254178
x = -4.694254178

Simplifying
x = -4.694254178


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.639079156, -4.694254178}

See similar equations:

| 9x^4+42x^3y-15x^2y^2= | | 6x+30+4x=20(x+3) | | 3x=8+3x-5 | | x-78=0 | | 2ln(2x)+6=14 | | (4u-1)(9+u)=0 | | -4y-8+2=2y+12 | | 2x+10=5+7x | | a=0.02+1.2 | | 2x+10=5-7x | | 25x^3-10x^2+15x-6= | | 0=-4x^2+8x+9 | | 8+6=2 | | 6+3v-v=6+2v+2 | | 8y-8*-0.25=10 | | 100(1+r)(1+r)=144 | | r^2+2r-144=0 | | -8x+8*-0.25=10 | | 7^6m*7^6m/7^-9m | | 2*(x^2)-70x+485=0 | | ((5Y+7)/3)=((2Y+5)/5)+14 | | 5LN(x+4.2)=6.2 | | 4.4m+6.4=8.8m-1.8 | | ab^3(2a-9a^2b+3b)= | | -2(6d+3)= | | 4ln(x+4.5)=3.4 | | x/2-6/x+2 | | 5y-2y+y+44=7y+50-5y | | 5(6)t-14=1 | | y^3+4y^2=9y+36 | | 8-20t^1/3=0 | | 5-24t^1/3=0 |

Equations solver categories