4(25x^2-254x+311)=0

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Solution for 4(25x^2-254x+311)=0 equation: 


Simplifying
4(25x2 + -254x + 311) = 0

Reorder the terms:
4(311 + -254x + 25x2) = 0
(311 * 4 + -254x * 4 + 25x2 * 4) = 0
(1244 + -1016x + 100x2) = 0

Solving
1244 + -1016x + 100x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(311 + -254x + 25x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(311 + -254x + 25x2)' equal to zero and attempt to solve:

Simplifying
311 + -254x + 25x2 = 0

Solving
311 + -254x + 25x2 = 0

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

Divide each side by '25'.
12.44 + -10.16x + x2 = 0

Move the constant term to the right:

Add '-12.44' to each side of the equation.
12.44 + -10.16x + -12.44 + x2 = 0 + -12.44

Reorder the terms:
12.44 + -12.44 + -10.16x + x2 = 0 + -12.44

Combine like terms: 12.44 + -12.44 = 0.00
0.00 + -10.16x + x2 = 0 + -12.44
-10.16x + x2 = 0 + -12.44

Combine like terms: 0 + -12.44 = -12.44
-10.16x + x2 = -12.44

The x term is -10.16x.  Take half its coefficient (-5.08).
Square it (25.8064) and add it to both sides.

Add '25.8064' to each side of the equation.
-10.16x + 25.8064 + x2 = -12.44 + 25.8064

Reorder the terms:
25.8064 + -10.16x + x2 = -12.44 + 25.8064

Combine like terms: -12.44 + 25.8064 = 13.3664
25.8064 + -10.16x + x2 = 13.3664

Factor a perfect square on the left side:
(x + -5.08)(x + -5.08) = 13.3664

Calculate the square root of the right side: 3.656008753

Break this problem into two subproblems by setting 
(x + -5.08) equal to 3.656008753 and -3.656008753.


Subproblem 1
x + -5.08 = 3.656008753

Simplifying
x + -5.08 = 3.656008753

Reorder the terms:
-5.08 + x = 3.656008753

Solving
-5.08 + x = 3.656008753

Solving for variable 'x'.

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

Add '5.08' to each side of the equation.
-5.08 + 5.08 + x = 3.656008753 + 5.08

Combine like terms: -5.08 + 5.08 = 0.00
0.00 + x = 3.656008753 + 5.08
x = 3.656008753 + 5.08

Combine like terms: 3.656008753 + 5.08 = 8.736008753
x = 8.736008753

Simplifying
x = 8.736008753


Subproblem 2
x + -5.08 = -3.656008753

Simplifying
x + -5.08 = -3.656008753

Reorder the terms:
-5.08 + x = -3.656008753

Solving
-5.08 + x = -3.656008753

Solving for variable 'x'.

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

Add '5.08' to each side of the equation.
-5.08 + 5.08 + x = -3.656008753 + 5.08

Combine like terms: -5.08 + 5.08 = 0.00
0.00 + x = -3.656008753 + 5.08
x = -3.656008753 + 5.08

Combine like terms: -3.656008753 + 5.08 = 1.423991247
x = 1.423991247

Simplifying
x = 1.423991247


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.736008753, 1.423991247}
Solution
x = {8.736008753, 1.423991247}

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