4x^2-600000x+2200000=0

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Solution for 4x^2-600000x+2200000=0 equation: 


Simplifying
4x2 + -600000x + 2200000 = 0

Reorder the terms:
2200000 + -600000x + 4x2 = 0

Solving
2200000 + -600000x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(550000 + -150000x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(550000 + -150000x + x2)' equal to zero and attempt to solve:

Simplifying
550000 + -150000x + x2 = 0

Solving
550000 + -150000x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-550000' to each side of the equation.
550000 + -150000x + -550000 + x2 = 0 + -550000

Reorder the terms:
550000 + -550000 + -150000x + x2 = 0 + -550000

Combine like terms: 550000 + -550000 = 0
0 + -150000x + x2 = 0 + -550000
-150000x + x2 = 0 + -550000

Combine like terms: 0 + -550000 = -550000
-150000x + x2 = -550000

The x term is -150000x.  Take half its coefficient (-75000).
Square it (5625000000) and add it to both sides.

Add '5625000000' to each side of the equation.
-150000x + 5625000000 + x2 = -550000 + 5625000000

Reorder the terms:
5625000000 + -150000x + x2 = -550000 + 5625000000

Combine like terms: -550000 + 5625000000 = 5624450000
5625000000 + -150000x + x2 = 5624450000

Factor a perfect square on the left side:
(x + -75000)(x + -75000) = 5624450000

Calculate the square root of the right side: 74996.333243699

Break this problem into two subproblems by setting 
(x + -75000) equal to 74996.333243699 and -74996.333243699.


Subproblem 1
x + -75000 = 74996.333243699

Simplifying
x + -75000 = 74996.333243699

Reorder the terms:
-75000 + x = 74996.333243699

Solving
-75000 + x = 74996.333243699

Solving for variable 'x'.

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

Add '75000' to each side of the equation.
-75000 + 75000 + x = 74996.333243699 + 75000

Combine like terms: -75000 + 75000 = 0
0 + x = 74996.333243699 + 75000
x = 74996.333243699 + 75000

Combine like terms: 74996.333243699 + 75000 = 149996.333243699
x = 149996.333243699

Simplifying
x = 149996.333243699


Subproblem 2
x + -75000 = -74996.333243699

Simplifying
x + -75000 = -74996.333243699

Reorder the terms:
-75000 + x = -74996.333243699

Solving
-75000 + x = -74996.333243699

Solving for variable 'x'.

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

Add '75000' to each side of the equation.
-75000 + 75000 + x = -74996.333243699 + 75000

Combine like terms: -75000 + 75000 = 0
0 + x = -74996.333243699 + 75000
x = -74996.333243699 + 75000

Combine like terms: -74996.333243699 + 75000 = 3.666756301
x = 3.666756301

Simplifying
x = 3.666756301


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {149996.333243699, 3.666756301}
Solution
x = {149996.333243699, 3.666756301}

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