2x^2-72x+8=0

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Solution for 2x^2-72x+8=0 equation: 


Simplifying
2x2 + -72x + 8 = 0

Reorder the terms:
8 + -72x + 2x2 = 0

Solving
8 + -72x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -36x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -36x + x2)' equal to zero and attempt to solve:

Simplifying
4 + -36x + x2 = 0

Solving
4 + -36x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -36x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -36x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -36x + x2 = 0 + -4
-36x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-36x + x2 = -4

The x term is -36x.  Take half its coefficient (-18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
-36x + 324 + x2 = -4 + 324

Reorder the terms:
324 + -36x + x2 = -4 + 324

Combine like terms: -4 + 324 = 320
324 + -36x + x2 = 320

Factor a perfect square on the left side:
(x + -18)(x + -18) = 320

Calculate the square root of the right side: 17.88854382

Break this problem into two subproblems by setting 
(x + -18) equal to 17.88854382 and -17.88854382.


Subproblem 1
x + -18 = 17.88854382

Simplifying
x + -18 = 17.88854382

Reorder the terms:
-18 + x = 17.88854382

Solving
-18 + x = 17.88854382

Solving for variable 'x'.

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

Add '18' to each side of the equation.
-18 + 18 + x = 17.88854382 + 18

Combine like terms: -18 + 18 = 0
0 + x = 17.88854382 + 18
x = 17.88854382 + 18

Combine like terms: 17.88854382 + 18 = 35.88854382
x = 35.88854382

Simplifying
x = 35.88854382


Subproblem 2
x + -18 = -17.88854382

Simplifying
x + -18 = -17.88854382

Reorder the terms:
-18 + x = -17.88854382

Solving
-18 + x = -17.88854382

Solving for variable 'x'.

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

Add '18' to each side of the equation.
-18 + 18 + x = -17.88854382 + 18

Combine like terms: -18 + 18 = 0
0 + x = -17.88854382 + 18
x = -17.88854382 + 18

Combine like terms: -17.88854382 + 18 = 0.11145618
x = 0.11145618

Simplifying
x = 0.11145618


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35.88854382, 0.11145618}
Solution
x = {35.88854382, 0.11145618}

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