4x^2-200x+200=0

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


Simplifying
4x2 + -200x + 200 = 0

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

Solving
200 + -200x + 4x2 = 0

Solving for variable 'x'.

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

Ignore the factor 4.

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

Simplifying
50 + -50x + x2 = 0

Solving
50 + -50x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -50 + 625

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

Combine like terms: -50 + 625 = 575
625 + -50x + x2 = 575

Factor a perfect square on the left side:
(x + -25)(x + -25) = 575

Calculate the square root of the right side: 23.979157617

Break this problem into two subproblems by setting 
(x + -25) equal to 23.979157617 and -23.979157617.


Subproblem 1
x + -25 = 23.979157617

Simplifying
x + -25 = 23.979157617

Reorder the terms:
-25 + x = 23.979157617

Solving
-25 + x = 23.979157617

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 = 23.979157617 + 25

Combine like terms: -25 + 25 = 0
0 + x = 23.979157617 + 25
x = 23.979157617 + 25

Combine like terms: 23.979157617 + 25 = 48.979157617
x = 48.979157617

Simplifying
x = 48.979157617


Subproblem 2
x + -25 = -23.979157617

Simplifying
x + -25 = -23.979157617

Reorder the terms:
-25 + x = -23.979157617

Solving
-25 + x = -23.979157617

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 = -23.979157617 + 25

Combine like terms: -25 + 25 = 0
0 + x = -23.979157617 + 25
x = -23.979157617 + 25

Combine like terms: -23.979157617 + 25 = 1.020842383
x = 1.020842383

Simplifying
x = 1.020842383


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {48.979157617, 1.020842383}
Solution
x = {48.979157617, 1.020842383}

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