2x^2-40x+96=0

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Solution for 2x^2-40x+96=0 equation: 


Simplifying
2x2 + -40x + 96 = 0

Reorder the terms:
96 + -40x + 2x2 = 0

Solving
96 + -40x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(48 + -20x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(48 + -20x + x2)' equal to zero and attempt to solve:

Simplifying
48 + -20x + x2 = 0

Solving
48 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-48' to each side of the equation.
48 + -20x + -48 + x2 = 0 + -48

Reorder the terms:
48 + -48 + -20x + x2 = 0 + -48

Combine like terms: 48 + -48 = 0
0 + -20x + x2 = 0 + -48
-20x + x2 = 0 + -48

Combine like terms: 0 + -48 = -48
-20x + x2 = -48

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -48 + 100

Reorder the terms:
100 + -20x + x2 = -48 + 100

Combine like terms: -48 + 100 = 52
100 + -20x + x2 = 52

Factor a perfect square on the left side:
(x + -10)(x + -10) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(x + -10) equal to 7.211102551 and -7.211102551.


Subproblem 1
x + -10 = 7.211102551

Simplifying
x + -10 = 7.211102551

Reorder the terms:
-10 + x = 7.211102551

Solving
-10 + x = 7.211102551

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 7.211102551 + 10

Combine like terms: -10 + 10 = 0
0 + x = 7.211102551 + 10
x = 7.211102551 + 10

Combine like terms: 7.211102551 + 10 = 17.211102551
x = 17.211102551

Simplifying
x = 17.211102551


Subproblem 2
x + -10 = -7.211102551

Simplifying
x + -10 = -7.211102551

Reorder the terms:
-10 + x = -7.211102551

Solving
-10 + x = -7.211102551

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -7.211102551 + 10

Combine like terms: -10 + 10 = 0
0 + x = -7.211102551 + 10
x = -7.211102551 + 10

Combine like terms: -7.211102551 + 10 = 2.788897449
x = 2.788897449

Simplifying
x = 2.788897449


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.211102551, 2.788897449}
Solution
x = {17.211102551, 2.788897449}

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