4x^2-200x-0.9=0

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Solution for 4x^2-200x-0.9=0 equation: 


Simplifying
4x2 + -200x + -0.9 = 0

Reorder the terms:
-0.9 + -200x + 4x2 = 0

Solving
-0.9 + -200x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-0.225 + -50x + x2 = 0

Move the constant term to the right:

Add '0.225' to each side of the equation.
-0.225 + -50x + 0.225 + x2 = 0 + 0.225

Reorder the terms:
-0.225 + 0.225 + -50x + x2 = 0 + 0.225

Combine like terms: -0.225 + 0.225 = 0.000
0.000 + -50x + x2 = 0 + 0.225
-50x + x2 = 0 + 0.225

Combine like terms: 0 + 0.225 = 0.225
-50x + x2 = 0.225

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 = 0.225 + 625

Reorder the terms:
625 + -50x + x2 = 0.225 + 625

Combine like terms: 0.225 + 625 = 625.225
625 + -50x + x2 = 625.225

Factor a perfect square on the left side:
(x + -25)(x + -25) = 625.225

Calculate the square root of the right side: 25.004499595

Break this problem into two subproblems by setting 
(x + -25) equal to 25.004499595 and -25.004499595.


Subproblem 1
x + -25 = 25.004499595

Simplifying
x + -25 = 25.004499595

Reorder the terms:
-25 + x = 25.004499595

Solving
-25 + x = 25.004499595

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 = 25.004499595 + 25

Combine like terms: -25 + 25 = 0
0 + x = 25.004499595 + 25
x = 25.004499595 + 25

Combine like terms: 25.004499595 + 25 = 50.004499595
x = 50.004499595

Simplifying
x = 50.004499595


Subproblem 2
x + -25 = -25.004499595

Simplifying
x + -25 = -25.004499595

Reorder the terms:
-25 + x = -25.004499595

Solving
-25 + x = -25.004499595

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 = -25.004499595 + 25

Combine like terms: -25 + 25 = 0
0 + x = -25.004499595 + 25
x = -25.004499595 + 25

Combine like terms: -25.004499595 + 25 = -0.004499595
x = -0.004499595

Simplifying
x = -0.004499595


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {50.004499595, -0.004499595}

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