4x^2-50x+40=0

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Solution for 4x^2-50x+40=0 equation: 


Simplifying
4x2 + -50x + 40 = 0

Reorder the terms:
40 + -50x + 4x2 = 0

Solving
40 + -50x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + -25x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(20 + -25x + 2x2)' equal to zero and attempt to solve:

Simplifying
20 + -25x + 2x2 = 0

Solving
20 + -25x + 2x2 = 0

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

Divide each side by '2'.
10 + -12.5x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -12.5x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -12.5x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -12.5x + x2 = 0 + -10
-12.5x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-12.5x + x2 = -10

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = -10 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = -10 + 39.0625

Combine like terms: -10 + 39.0625 = 29.0625
39.0625 + -12.5x + x2 = 29.0625

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 29.0625

Calculate the square root of the right side: 5.390964663

Break this problem into two subproblems by setting 
(x + -6.25) equal to 5.390964663 and -5.390964663.


Subproblem 1
x + -6.25 = 5.390964663

Simplifying
x + -6.25 = 5.390964663

Reorder the terms:
-6.25 + x = 5.390964663

Solving
-6.25 + x = 5.390964663

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = 5.390964663 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = 5.390964663 + 6.25
x = 5.390964663 + 6.25

Combine like terms: 5.390964663 + 6.25 = 11.640964663
x = 11.640964663

Simplifying
x = 11.640964663


Subproblem 2
x + -6.25 = -5.390964663

Simplifying
x + -6.25 = -5.390964663

Reorder the terms:
-6.25 + x = -5.390964663

Solving
-6.25 + x = -5.390964663

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = -5.390964663 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = -5.390964663 + 6.25
x = -5.390964663 + 6.25

Combine like terms: -5.390964663 + 6.25 = 0.859035337
x = 0.859035337

Simplifying
x = 0.859035337


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.640964663, 0.859035337}
Solution
x = {11.640964663, 0.859035337}

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