600x^2-800x-32400=0

Simple and best practice solution for 600x^2-800x-32400=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 600x^2-800x-32400=0 equation: 


Simplifying
600x2 + -800x + -32400 = 0

Reorder the terms:
-32400 + -800x + 600x2 = 0

Solving
-32400 + -800x + 600x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '200'.
200(-162 + -4x + 3x2) = 0

Ignore the factor 200.

Subproblem 1
Set the factor '(-162 + -4x + 3x2)' equal to zero and attempt to solve:

Simplifying
-162 + -4x + 3x2 = 0

Solving
-162 + -4x + 3x2 = 0

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

Divide each side by '3'.
-54 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + -1.333333333x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + -1.333333333x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + -1.333333333x + x2 = 0 + 54
-1.333333333x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
-1.333333333x + x2 = 54

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 54 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 54 + 0.4444444442

Combine like terms: 54 + 0.4444444442 = 54.4444444442
0.4444444442 + -1.333333333x + x2 = 54.4444444442

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 54.4444444442

Calculate the square root of the right side: 7.378647874

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 7.378647874 and -7.378647874.


Subproblem 1
x + -0.6666666665 = 7.378647874

Simplifying
x + -0.6666666665 = 7.378647874

Reorder the terms:
-0.6666666665 + x = 7.378647874

Solving
-0.6666666665 + x = 7.378647874

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 7.378647874 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 7.378647874 + 0.6666666665
x = 7.378647874 + 0.6666666665

Combine like terms: 7.378647874 + 0.6666666665 = 8.0453145405
x = 8.0453145405

Simplifying
x = 8.0453145405


Subproblem 2
x + -0.6666666665 = -7.378647874

Simplifying
x + -0.6666666665 = -7.378647874

Reorder the terms:
-0.6666666665 + x = -7.378647874

Solving
-0.6666666665 + x = -7.378647874

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -7.378647874 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -7.378647874 + 0.6666666665
x = -7.378647874 + 0.6666666665

Combine like terms: -7.378647874 + 0.6666666665 = -6.7119812075
x = -6.7119812075

Simplifying
x = -6.7119812075


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.0453145405, -6.7119812075}
Solution
x = {8.0453145405, -6.7119812075}

See similar equations:

| 2c+3x=23 | | 5r-6p=12 | | 4m+6=15m | | 2y^2+4x+2=0 | | 1/2(y-1)=4y | | 3x-5(x-3)=-4+5x-9 | | 6a-2b=9 | | (2h)+(2h)=180 | | (2h)+(2h)= | | 2x-1=5x-15 | | (2h)+(2h)=40 | | (-2)-(-7)=5 | | 0.3b+3=0.5b | | 5(3x-1)+2(4-5x)-2(2x+4)=-7 | | (63x^5-28x^4-35x^2)/(-7x^2) | | -3(5p+3)-2(6-14p)-3(2+4p)=0 | | 1p-1q+6r=5a+3g-7c | | 11y=-27 | | xy+5ay+10ac+2xc= | | (5k-3)+(9+k)=180 | | 6x^2-11x-19= | | 5x-3=-3x+10 | | (9x)+(5x)+(9+x)= | | (x+15)+(4x-20)= | | 40k+100=30k+1q | | 4.4q-1.3-5.6q=0.2q-1.3 | | X=95+.05X | | 4(x-1)+3(x-2)=4 | | 7m-32=47 | | 7(w-3)=-2w-48 | | 3T+3+5T-7T=3+2 | | 10(c-1)=2(2c-5) |

Equations solver categories