4x^2+1000x=81000

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Solution for 4x^2+1000x=81000 equation: 


Simplifying
4x2 + 1000x = 81000

Reorder the terms:
1000x + 4x2 = 81000

Solving
1000x + 4x2 = 81000

Solving for variable 'x'.

Reorder the terms:
-81000 + 1000x + 4x2 = 81000 + -81000

Combine like terms: 81000 + -81000 = 0
-81000 + 1000x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-20250 + 250x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-20250 + 250x + x2)' equal to zero and attempt to solve:

Simplifying
-20250 + 250x + x2 = 0

Solving
-20250 + 250x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20250' to each side of the equation.
-20250 + 250x + 20250 + x2 = 0 + 20250

Reorder the terms:
-20250 + 20250 + 250x + x2 = 0 + 20250

Combine like terms: -20250 + 20250 = 0
0 + 250x + x2 = 0 + 20250
250x + x2 = 0 + 20250

Combine like terms: 0 + 20250 = 20250
250x + x2 = 20250

The x term is 250x.  Take half its coefficient (125).
Square it (15625) and add it to both sides.

Add '15625' to each side of the equation.
250x + 15625 + x2 = 20250 + 15625

Reorder the terms:
15625 + 250x + x2 = 20250 + 15625

Combine like terms: 20250 + 15625 = 35875
15625 + 250x + x2 = 35875

Factor a perfect square on the left side:
(x + 125)(x + 125) = 35875

Calculate the square root of the right side: 189.406969249

Break this problem into two subproblems by setting 
(x + 125) equal to 189.406969249 and -189.406969249.


Subproblem 1
x + 125 = 189.406969249

Simplifying
x + 125 = 189.406969249

Reorder the terms:
125 + x = 189.406969249

Solving
125 + x = 189.406969249

Solving for variable 'x'.

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

Add '-125' to each side of the equation.
125 + -125 + x = 189.406969249 + -125

Combine like terms: 125 + -125 = 0
0 + x = 189.406969249 + -125
x = 189.406969249 + -125

Combine like terms: 189.406969249 + -125 = 64.406969249
x = 64.406969249

Simplifying
x = 64.406969249


Subproblem 2
x + 125 = -189.406969249

Simplifying
x + 125 = -189.406969249

Reorder the terms:
125 + x = -189.406969249

Solving
125 + x = -189.406969249

Solving for variable 'x'.

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

Add '-125' to each side of the equation.
125 + -125 + x = -189.406969249 + -125

Combine like terms: 125 + -125 = 0
0 + x = -189.406969249 + -125
x = -189.406969249 + -125

Combine like terms: -189.406969249 + -125 = -314.406969249
x = -314.406969249

Simplifying
x = -314.406969249


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {64.406969249, -314.406969249}
Solution
x = {64.406969249, -314.406969249}

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