3x^2+x-22=0

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


Simplifying
3x2 + x + -22 = 0

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

Solving
-22 + x + 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 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '7.333333333' to each side of the equation.
-7.333333333 + 0.3333333333x + 7.333333333 + x2 = 0 + 7.333333333

Reorder the terms:
-7.333333333 + 7.333333333 + 0.3333333333x + x2 = 0 + 7.333333333

Combine like terms: -7.333333333 + 7.333333333 = 0.000000000
0.000000000 + 0.3333333333x + x2 = 0 + 7.333333333
0.3333333333x + x2 = 0 + 7.333333333

Combine like terms: 0 + 7.333333333 = 7.333333333
0.3333333333x + x2 = 7.333333333

The x term is x.  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.
0.3333333333x + 0.25 + x2 = 7.333333333 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = 7.333333333 + 0.25

Combine like terms: 7.333333333 + 0.25 = 7.583333333
0.25 + 0.3333333333x + x2 = 7.583333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 7.583333333

Calculate the square root of the right side: 2.753785274

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.753785274 and -2.753785274.


Subproblem 1
x + 0.5 = 2.753785274

Simplifying
x + 0.5 = 2.753785274

Reorder the terms:
0.5 + x = 2.753785274

Solving
0.5 + x = 2.753785274

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 2.753785274 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.753785274 + -0.5
x = 2.753785274 + -0.5

Combine like terms: 2.753785274 + -0.5 = 2.253785274
x = 2.253785274

Simplifying
x = 2.253785274


Subproblem 2
x + 0.5 = -2.753785274

Simplifying
x + 0.5 = -2.753785274

Reorder the terms:
0.5 + x = -2.753785274

Solving
0.5 + x = -2.753785274

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -2.753785274 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.753785274 + -0.5
x = -2.753785274 + -0.5

Combine like terms: -2.753785274 + -0.5 = -3.253785274
x = -3.253785274

Simplifying
x = -3.253785274


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.253785274, -3.253785274}

See similar equations:

| 3n-7=12n-12 | | 3n/5=4n-102 | | 2y+45=13 | | Y+80=3y | | ln(x+5)+ln(x+3)=ln(8) | | 4+3y=42 | | 4+y=18 | | 2+3y=42 | | 3x^2+4x-63=0 | | g-2-1g+.5=0 | | 2+y=18 | | -2m+5=6m-11 | | 0+3y=42 | | 0=x^4+6x^3+44x^2+216x+288 | | 5y+3-4y-8=6+9 | | 0+y=18 | | g-2=g-.5 | | 6m-2=3m-4 | | -18b+7y/6b | | -18b+74/6b | | 2(9)+3y=24 | | 5y+7=4y+2 | | 2(9)=9y | | 3x^2+x-6x=3 | | 2(8)+3y=24 | | solvex^4-7x^2-18=0 | | -6-4.8m=-5m-4.8 | | 3c+13=2c+14 | | factorx^4-7x^2-18=0 | | 2(8)=9y | | 4b+24=2b+12 | | 2(0)+3y=24 |

Equations solver categories