4x^2+31x+22=0

Simple and best practice solution for 4x^2+31x+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 4x^2+31x+22=0 equation: 


Simplifying
4x2 + 31x + 22 = 0

Reorder the terms:
22 + 31x + 4x2 = 0

Solving
22 + 31x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
5.5 + 7.75x + x2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + 7.75x + -5.5 + x2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + 7.75x + x2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + 7.75x + x2 = 0 + -5.5
7.75x + x2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
7.75x + x2 = -5.5

The x term is 7.75x.  Take half its coefficient (3.875).
Square it (15.015625) and add it to both sides.

Add '15.015625' to each side of the equation.
7.75x + 15.015625 + x2 = -5.5 + 15.015625

Reorder the terms:
15.015625 + 7.75x + x2 = -5.5 + 15.015625

Combine like terms: -5.5 + 15.015625 = 9.515625
15.015625 + 7.75x + x2 = 9.515625

Factor a perfect square on the left side:
(x + 3.875)(x + 3.875) = 9.515625

Calculate the square root of the right side: 3.08474067

Break this problem into two subproblems by setting 
(x + 3.875) equal to 3.08474067 and -3.08474067.


Subproblem 1
x + 3.875 = 3.08474067

Simplifying
x + 3.875 = 3.08474067

Reorder the terms:
3.875 + x = 3.08474067

Solving
3.875 + x = 3.08474067

Solving for variable 'x'.

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

Add '-3.875' to each side of the equation.
3.875 + -3.875 + x = 3.08474067 + -3.875

Combine like terms: 3.875 + -3.875 = 0.000
0.000 + x = 3.08474067 + -3.875
x = 3.08474067 + -3.875

Combine like terms: 3.08474067 + -3.875 = -0.79025933
x = -0.79025933

Simplifying
x = -0.79025933


Subproblem 2
x + 3.875 = -3.08474067

Simplifying
x + 3.875 = -3.08474067

Reorder the terms:
3.875 + x = -3.08474067

Solving
3.875 + x = -3.08474067

Solving for variable 'x'.

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

Add '-3.875' to each side of the equation.
3.875 + -3.875 + x = -3.08474067 + -3.875

Combine like terms: 3.875 + -3.875 = 0.000
0.000 + x = -3.08474067 + -3.875
x = -3.08474067 + -3.875

Combine like terms: -3.08474067 + -3.875 = -6.95974067
x = -6.95974067

Simplifying
x = -6.95974067


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.79025933, -6.95974067}

See similar equations:

| (4x^2+31x+22)/(x+7) | | 9a^13b^20=0 | | 1/2(n-6)=19 | | 8x-12=-4x+12 | | log(x)+log(8)=2 | | 63=0.5(2x)(2x+4) | | y=pi/(7x^2-8) | | 8x-12=4x+12 | | 1/3x=92 | | x+9+x+3+x^2-3x+3x-3=57 | | (x+3)(2x-2)=(2x+3)(x+1) | | 18-2x=x-25 | | y=(2x-5)(5x^3-x^2+1) | | ln(x+3)-1=0 | | -3y+4+5y= | | 1000(n+20)=100 | | 700(n+20)=100 | | 0.15x=63 | | 500(n+20)=100 | | 4-3x/7-x+3/7=x+8 | | 4-3x/7-x+3/70x+8 | | -90t=-3500+60t | | (n-7)*9=81 | | 17=x-14+12-11 | | -90=-3500+60t | | 300(n+20)=100 | | -90+-3500+60= | | 2x^2+(-4)+7x^2+(-4x)+(-7)= | | 250(n+20)=100 | | 18x+35=35+18x | | 200(n+20)=100 | | w^2+26w-855=0 |

Equations solver categories