3x^2+20x+22=0

Simple and best practice solution for 3x^2+20x+22=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+20x+22=0 equation: 


Simplifying
3x2 + 20x + 22 = 0

Reorder the terms:
22 + 20x + 3x2 = 0

Solving
22 + 20x + 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'.
7.333333333 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '-7.333333333' to each side of the equation.
7.333333333 + 6.666666667x + -7.333333333 + x2 = 0 + -7.333333333

Reorder the terms:
7.333333333 + -7.333333333 + 6.666666667x + x2 = 0 + -7.333333333

Combine like terms: 7.333333333 + -7.333333333 = 0.000000000
0.000000000 + 6.666666667x + x2 = 0 + -7.333333333
6.666666667x + x2 = 0 + -7.333333333

Combine like terms: 0 + -7.333333333 = -7.333333333
6.666666667x + x2 = -7.333333333

The x term is 6.666666667x.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667x + 11.11111112 + x2 = -7.333333333 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = -7.333333333 + 11.11111112

Combine like terms: -7.333333333 + 11.11111112 = 3.777777787
11.11111112 + 6.666666667x + x2 = 3.777777787

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 3.777777787

Calculate the square root of the right side: 1.943650634

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 1.943650634 and -1.943650634.


Subproblem 1
x + 3.333333334 = 1.943650634

Simplifying
x + 3.333333334 = 1.943650634

Reorder the terms:
3.333333334 + x = 1.943650634

Solving
3.333333334 + x = 1.943650634

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = 1.943650634 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 1.943650634 + -3.333333334
x = 1.943650634 + -3.333333334

Combine like terms: 1.943650634 + -3.333333334 = -1.3896827
x = -1.3896827

Simplifying
x = -1.3896827


Subproblem 2
x + 3.333333334 = -1.943650634

Simplifying
x + 3.333333334 = -1.943650634

Reorder the terms:
3.333333334 + x = -1.943650634

Solving
3.333333334 + x = -1.943650634

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = -1.943650634 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -1.943650634 + -3.333333334
x = -1.943650634 + -3.333333334

Combine like terms: -1.943650634 + -3.333333334 = -5.276983968
x = -5.276983968

Simplifying
x = -5.276983968


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.3896827, -5.276983968}

See similar equations:

| 3xy+6x=18 | | 5(x+7)+8=9x-4(x-5) | | 1/2*-4= | | 5(x+7)+8=9x-4(4x-5) | | 4(2x+7)=3(x-1) | | -8x+2x-6=-5x+7x | | w+2/3=3 | | 4x^2=178 | | 5-2x+6=1 | | ln(y-4)-ln(9)=x+ln(x) | | 6(3x+1)=7(2x-3) | | -3x(x-6)=18 | | 3(-2)+4[14-4]= | | y*y=5*5+(5*3)*(5*3) | | 2m-10=4-2(m-5)-12 | | (6x-41)2=180 | | 6x-41=180 | | 11(3x-2)=5(6x-5) | | (6x+-41)*2+(3x+22)2=360 | | -56+8= | | 4(3y-7)-(13y-2)= | | (6x-41)2+(3x+22)=360 | | -3x(x-6)=6 | | (6x-41)2+(3x+22)2=360 | | xy+15x=(y+15) | | 16y^2+48y=0 | | -7+-33n= | | z-(2z-[3z-(4z-5z)-6z]-7z)-8z= | | -35n+2n= | | 8-2(3m-7)=-5m+11m+3 | | 35n+2n= | | x^4-7x-44=0 |

Equations solver categories