4x^2+200x+804=0

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Solution for 4x^2+200x+804=0 equation: 


Simplifying
4x2 + 200x + 804 = 0

Reorder the terms:
804 + 200x + 4x2 = 0

Solving
804 + 200x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(201 + 50x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(201 + 50x + x2)' equal to zero and attempt to solve:

Simplifying
201 + 50x + x2 = 0

Solving
201 + 50x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-201' to each side of the equation.
201 + 50x + -201 + x2 = 0 + -201

Reorder the terms:
201 + -201 + 50x + x2 = 0 + -201

Combine like terms: 201 + -201 = 0
0 + 50x + x2 = 0 + -201
50x + x2 = 0 + -201

Combine like terms: 0 + -201 = -201
50x + x2 = -201

The x term is 50x.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50x + 625 + x2 = -201 + 625

Reorder the terms:
625 + 50x + x2 = -201 + 625

Combine like terms: -201 + 625 = 424
625 + 50x + x2 = 424

Factor a perfect square on the left side:
(x + 25)(x + 25) = 424

Calculate the square root of the right side: 20.591260282

Break this problem into two subproblems by setting 
(x + 25) equal to 20.591260282 and -20.591260282.


Subproblem 1
x + 25 = 20.591260282

Simplifying
x + 25 = 20.591260282

Reorder the terms:
25 + x = 20.591260282

Solving
25 + x = 20.591260282

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = 20.591260282 + -25

Combine like terms: 25 + -25 = 0
0 + x = 20.591260282 + -25
x = 20.591260282 + -25

Combine like terms: 20.591260282 + -25 = -4.408739718
x = -4.408739718

Simplifying
x = -4.408739718


Subproblem 2
x + 25 = -20.591260282

Simplifying
x + 25 = -20.591260282

Reorder the terms:
25 + x = -20.591260282

Solving
25 + x = -20.591260282

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = -20.591260282 + -25

Combine like terms: 25 + -25 = 0
0 + x = -20.591260282 + -25
x = -20.591260282 + -25

Combine like terms: -20.591260282 + -25 = -45.591260282
x = -45.591260282

Simplifying
x = -45.591260282


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.408739718, -45.591260282}
Solution
x = {-4.408739718, -45.591260282}

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