4x^2+600x-4000=0

Simple and best practice solution for 4x^2+600x-4000=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+600x-4000=0 equation: 


Simplifying
4x2 + 600x + -4000 = 0

Reorder the terms:
-4000 + 600x + 4x2 = 0

Solving
-4000 + 600x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1000 + 150x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1000 + 150x + x2)' equal to zero and attempt to solve:

Simplifying
-1000 + 150x + x2 = 0

Solving
-1000 + 150x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1000' to each side of the equation.
-1000 + 150x + 1000 + x2 = 0 + 1000

Reorder the terms:
-1000 + 1000 + 150x + x2 = 0 + 1000

Combine like terms: -1000 + 1000 = 0
0 + 150x + x2 = 0 + 1000
150x + x2 = 0 + 1000

Combine like terms: 0 + 1000 = 1000
150x + x2 = 1000

The x term is 150x.  Take half its coefficient (75).
Square it (5625) and add it to both sides.

Add '5625' to each side of the equation.
150x + 5625 + x2 = 1000 + 5625

Reorder the terms:
5625 + 150x + x2 = 1000 + 5625

Combine like terms: 1000 + 5625 = 6625
5625 + 150x + x2 = 6625

Factor a perfect square on the left side:
(x + 75)(x + 75) = 6625

Calculate the square root of the right side: 81.39410298

Break this problem into two subproblems by setting 
(x + 75) equal to 81.39410298 and -81.39410298.


Subproblem 1
x + 75 = 81.39410298

Simplifying
x + 75 = 81.39410298

Reorder the terms:
75 + x = 81.39410298

Solving
75 + x = 81.39410298

Solving for variable 'x'.

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

Add '-75' to each side of the equation.
75 + -75 + x = 81.39410298 + -75

Combine like terms: 75 + -75 = 0
0 + x = 81.39410298 + -75
x = 81.39410298 + -75

Combine like terms: 81.39410298 + -75 = 6.39410298
x = 6.39410298

Simplifying
x = 6.39410298


Subproblem 2
x + 75 = -81.39410298

Simplifying
x + 75 = -81.39410298

Reorder the terms:
75 + x = -81.39410298

Solving
75 + x = -81.39410298

Solving for variable 'x'.

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

Add '-75' to each side of the equation.
75 + -75 + x = -81.39410298 + -75

Combine like terms: 75 + -75 = 0
0 + x = -81.39410298 + -75
x = -81.39410298 + -75

Combine like terms: -81.39410298 + -75 = -156.39410298
x = -156.39410298

Simplifying
x = -156.39410298


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.39410298, -156.39410298}
Solution
x = {6.39410298, -156.39410298}

See similar equations:

| 100x=7234.56(75) | | 3n^2-6n-45=0 | | 2304(3.14)=X | | 12b^2+17b+6=0 | | 2m^2+13m-24=0 | | 13-6f=31 | | 2(x+17)=400 | | n^2+23=0 | | 3c^2-10=13c | | 2x^2-16x+15=0 | | 2x^2+16x+15=0 | | =15y^2+26y+8 | | 53-(5x+11)=5(x+4)+x | | 6x+3y=54 | | p(x)=10x^3-6x^2+4x+8 | | 4w+12-10=16w-10 | | 49+49=225 | | 15(15)=x | | 3(3x-1.9)=7x-5.7 | | 0.4(3x+6)=1.1-(x+2) | | 4y-4+y+42=8y+40-5y | | 37-(2x+9)=2(x+9)+x | | 3z-(2z-5)=5 | | 2*x*x+3x-203238=0 | | 55(45+4)=x | | r^2=-6-5r | | w^2-17=0 | | 3y+11=0 | | -7x+11=0 | | 0.24y-0.6=0.14y+1-0.7y | | 36x=100(25) | | 36-11=x |

Equations solver categories