2x^2-32x+50=0

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Solution for 2x^2-32x+50=0 equation: 


Simplifying
2x2 + -32x + 50 = 0

Reorder the terms:
50 + -32x + 2x2 = 0

Solving
50 + -32x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + -16x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + -16x + x2)' equal to zero and attempt to solve:

Simplifying
25 + -16x + x2 = 0

Solving
25 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -16x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + -16x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -16x + x2 = 0 + -25
-16x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
-16x + x2 = -25

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -25 + 64

Reorder the terms:
64 + -16x + x2 = -25 + 64

Combine like terms: -25 + 64 = 39
64 + -16x + x2 = 39

Factor a perfect square on the left side:
(x + -8)(x + -8) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(x + -8) equal to 6.244997998 and -6.244997998.


Subproblem 1
x + -8 = 6.244997998

Simplifying
x + -8 = 6.244997998

Reorder the terms:
-8 + x = 6.244997998

Solving
-8 + x = 6.244997998

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 6.244997998 + 8

Combine like terms: -8 + 8 = 0
0 + x = 6.244997998 + 8
x = 6.244997998 + 8

Combine like terms: 6.244997998 + 8 = 14.244997998
x = 14.244997998

Simplifying
x = 14.244997998


Subproblem 2
x + -8 = -6.244997998

Simplifying
x + -8 = -6.244997998

Reorder the terms:
-8 + x = -6.244997998

Solving
-8 + x = -6.244997998

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -6.244997998 + 8

Combine like terms: -8 + 8 = 0
0 + x = -6.244997998 + 8
x = -6.244997998 + 8

Combine like terms: -6.244997998 + 8 = 1.755002002
x = 1.755002002

Simplifying
x = 1.755002002


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.244997998, 1.755002002}
Solution
x = {14.244997998, 1.755002002}

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