3X^2+22X-300=0

Simple and best practice solution for 3X^2+22X-300=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+22X-300=0 equation: 


Simplifying
3X2 + 22X + -300 = 0

Reorder the terms:
-300 + 22X + 3X2 = 0

Solving
-300 + 22X + 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'.
-100 + 7.333333333X + X2 = 0

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 7.333333333X + 100 + X2 = 0 + 100

Reorder the terms:
-100 + 100 + 7.333333333X + X2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 7.333333333X + X2 = 0 + 100
7.333333333X + X2 = 0 + 100

Combine like terms: 0 + 100 = 100
7.333333333X + X2 = 100

The X term is 7.333333333X.  Take half its coefficient (3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
7.333333333X + 13.44444445 + X2 = 100 + 13.44444445

Reorder the terms:
13.44444445 + 7.333333333X + X2 = 100 + 13.44444445

Combine like terms: 100 + 13.44444445 = 113.44444445
13.44444445 + 7.333333333X + X2 = 113.44444445

Factor a perfect square on the left side:
(X + 3.666666667)(X + 3.666666667) = 113.44444445

Calculate the square root of the right side: 10.651030206

Break this problem into two subproblems by setting 
(X + 3.666666667) equal to 10.651030206 and -10.651030206.


Subproblem 1
X + 3.666666667 = 10.651030206

Simplifying
X + 3.666666667 = 10.651030206

Reorder the terms:
3.666666667 + X = 10.651030206

Solving
3.666666667 + X = 10.651030206

Solving for variable 'X'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + X = 10.651030206 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + X = 10.651030206 + -3.666666667
X = 10.651030206 + -3.666666667

Combine like terms: 10.651030206 + -3.666666667 = 6.984363539
X = 6.984363539

Simplifying
X = 6.984363539


Subproblem 2
X + 3.666666667 = -10.651030206

Simplifying
X + 3.666666667 = -10.651030206

Reorder the terms:
3.666666667 + X = -10.651030206

Solving
3.666666667 + X = -10.651030206

Solving for variable 'X'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + X = -10.651030206 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + X = -10.651030206 + -3.666666667
X = -10.651030206 + -3.666666667

Combine like terms: -10.651030206 + -3.666666667 = -14.317696873
X = -14.317696873

Simplifying
X = -14.317696873


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {6.984363539, -14.317696873}

See similar equations:

| 2x^2-8x=-8 | | 15x^2-46x+35=0 | | x^2+2x-13=2 | | 8x+7=23 | | x^2+2x-13=0 | | 10z^2-9z-9= | | x^2-10x+29=0 | | x^2+6=5x | | x^2+8x+32=0 | | -8=w-(-8) | | x^2-4=2x | | 8x^2=72 | | -2-a+4=12 | | a=-1.805555556 | | 0.15x+.05(20-x)=.10(6) | | 14=0.1x | | (2x-1)*(8x-4)=-1 | | 5y+3=15 | | 2y=14-6x | | 5(2z-3)=9(z+4) | | 4(y-7)+2=-14 | | 5(n+3)-2=23 | | 2x+8y=3 | | 6(4m-7)=-18 | | 6(3m-2)=60 | | 6(2a-3)=30 | | -2x-3=-3 | | 6x+2=-28 | | 24.8x=-153.76 | | 4-3d=-23 | | 152=-16t^2+96t+12 | | 4+9a=31 |

Equations solver categories