4x^2-400x+1000=0

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Solution for 4x^2-400x+1000=0 equation: 


Simplifying
4x2 + -400x + 1000 = 0

Reorder the terms:
1000 + -400x + 4x2 = 0

Solving
1000 + -400x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(250 + -100x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(250 + -100x + x2)' equal to zero and attempt to solve:

Simplifying
250 + -100x + x2 = 0

Solving
250 + -100x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-250' to each side of the equation.
250 + -100x + -250 + x2 = 0 + -250

Reorder the terms:
250 + -250 + -100x + x2 = 0 + -250

Combine like terms: 250 + -250 = 0
0 + -100x + x2 = 0 + -250
-100x + x2 = 0 + -250

Combine like terms: 0 + -250 = -250
-100x + x2 = -250

The x term is -100x.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100x + 2500 + x2 = -250 + 2500

Reorder the terms:
2500 + -100x + x2 = -250 + 2500

Combine like terms: -250 + 2500 = 2250
2500 + -100x + x2 = 2250

Factor a perfect square on the left side:
(x + -50)(x + -50) = 2250

Calculate the square root of the right side: 47.434164903

Break this problem into two subproblems by setting 
(x + -50) equal to 47.434164903 and -47.434164903.


Subproblem 1
x + -50 = 47.434164903

Simplifying
x + -50 = 47.434164903

Reorder the terms:
-50 + x = 47.434164903

Solving
-50 + x = 47.434164903

Solving for variable 'x'.

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

Add '50' to each side of the equation.
-50 + 50 + x = 47.434164903 + 50

Combine like terms: -50 + 50 = 0
0 + x = 47.434164903 + 50
x = 47.434164903 + 50

Combine like terms: 47.434164903 + 50 = 97.434164903
x = 97.434164903

Simplifying
x = 97.434164903


Subproblem 2
x + -50 = -47.434164903

Simplifying
x + -50 = -47.434164903

Reorder the terms:
-50 + x = -47.434164903

Solving
-50 + x = -47.434164903

Solving for variable 'x'.

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

Add '50' to each side of the equation.
-50 + 50 + x = -47.434164903 + 50

Combine like terms: -50 + 50 = 0
0 + x = -47.434164903 + 50
x = -47.434164903 + 50

Combine like terms: -47.434164903 + 50 = 2.565835097
x = 2.565835097

Simplifying
x = 2.565835097


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {97.434164903, 2.565835097}
Solution
x = {97.434164903, 2.565835097}

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