4x^2+10000x-60000=0

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Solution for 4x^2+10000x-60000=0 equation: 


Simplifying
4x2 + 10000x + -60000 = 0

Reorder the terms:
-60000 + 10000x + 4x2 = 0

Solving
-60000 + 10000x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15000 + 2500x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-15000 + 2500x + x2)' equal to zero and attempt to solve:

Simplifying
-15000 + 2500x + x2 = 0

Solving
-15000 + 2500x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15000' to each side of the equation.
-15000 + 2500x + 15000 + x2 = 0 + 15000

Reorder the terms:
-15000 + 15000 + 2500x + x2 = 0 + 15000

Combine like terms: -15000 + 15000 = 0
0 + 2500x + x2 = 0 + 15000
2500x + x2 = 0 + 15000

Combine like terms: 0 + 15000 = 15000
2500x + x2 = 15000

The x term is 2500x.  Take half its coefficient (1250).
Square it (1562500) and add it to both sides.

Add '1562500' to each side of the equation.
2500x + 1562500 + x2 = 15000 + 1562500

Reorder the terms:
1562500 + 2500x + x2 = 15000 + 1562500

Combine like terms: 15000 + 1562500 = 1577500
1562500 + 2500x + x2 = 1577500

Factor a perfect square on the left side:
(x + 1250)(x + 1250) = 1577500

Calculate the square root of the right side: 1255.985668708

Break this problem into two subproblems by setting 
(x + 1250) equal to 1255.985668708 and -1255.985668708.


Subproblem 1
x + 1250 = 1255.985668708

Simplifying
x + 1250 = 1255.985668708

Reorder the terms:
1250 + x = 1255.985668708

Solving
1250 + x = 1255.985668708

Solving for variable 'x'.

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

Add '-1250' to each side of the equation.
1250 + -1250 + x = 1255.985668708 + -1250

Combine like terms: 1250 + -1250 = 0
0 + x = 1255.985668708 + -1250
x = 1255.985668708 + -1250

Combine like terms: 1255.985668708 + -1250 = 5.985668708
x = 5.985668708

Simplifying
x = 5.985668708


Subproblem 2
x + 1250 = -1255.985668708

Simplifying
x + 1250 = -1255.985668708

Reorder the terms:
1250 + x = -1255.985668708

Solving
1250 + x = -1255.985668708

Solving for variable 'x'.

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

Add '-1250' to each side of the equation.
1250 + -1250 + x = -1255.985668708 + -1250

Combine like terms: 1250 + -1250 = 0
0 + x = -1255.985668708 + -1250
x = -1255.985668708 + -1250

Combine like terms: -1255.985668708 + -1250 = -2505.985668708
x = -2505.985668708

Simplifying
x = -2505.985668708


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.985668708, -2505.985668708}
Solution
x = {5.985668708, -2505.985668708}

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