8(x^2-50x+48)=0

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Solution for 8(x^2-50x+48)=0 equation: 


Simplifying
8(x2 + -50x + 48) = 0

Reorder the terms:
8(48 + -50x + x2) = 0
(48 * 8 + -50x * 8 + x2 * 8) = 0
(384 + -400x + 8x2) = 0

Solving
384 + -400x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(48 + -50x + x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(48 + -50x + x2)' equal to zero and attempt to solve:

Simplifying
48 + -50x + x2 = 0

Solving
48 + -50x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-48' to each side of the equation.
48 + -50x + -48 + x2 = 0 + -48

Reorder the terms:
48 + -48 + -50x + x2 = 0 + -48

Combine like terms: 48 + -48 = 0
0 + -50x + x2 = 0 + -48
-50x + x2 = 0 + -48

Combine like terms: 0 + -48 = -48
-50x + x2 = -48

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 = -48 + 625

Reorder the terms:
625 + -50x + x2 = -48 + 625

Combine like terms: -48 + 625 = 577
625 + -50x + x2 = 577

Factor a perfect square on the left side:
(x + -25)(x + -25) = 577

Calculate the square root of the right side: 24.020824299

Break this problem into two subproblems by setting 
(x + -25) equal to 24.020824299 and -24.020824299.


Subproblem 1
x + -25 = 24.020824299

Simplifying
x + -25 = 24.020824299

Reorder the terms:
-25 + x = 24.020824299

Solving
-25 + x = 24.020824299

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 = 24.020824299 + 25

Combine like terms: -25 + 25 = 0
0 + x = 24.020824299 + 25
x = 24.020824299 + 25

Combine like terms: 24.020824299 + 25 = 49.020824299
x = 49.020824299

Simplifying
x = 49.020824299


Subproblem 2
x + -25 = -24.020824299

Simplifying
x + -25 = -24.020824299

Reorder the terms:
-25 + x = -24.020824299

Solving
-25 + x = -24.020824299

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 = -24.020824299 + 25

Combine like terms: -25 + 25 = 0
0 + x = -24.020824299 + 25
x = -24.020824299 + 25

Combine like terms: -24.020824299 + 25 = 0.979175701
x = 0.979175701

Simplifying
x = 0.979175701


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {49.020824299, 0.979175701}
Solution
x = {49.020824299, 0.979175701}

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