x^2-38x+324=0

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Solution for x^2-38x+324=0 equation: 


Simplifying
x2 + -38x + 324 = 0

Reorder the terms:
324 + -38x + x2 = 0

Solving
324 + -38x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-324' to each side of the equation.
324 + -38x + -324 + x2 = 0 + -324

Reorder the terms:
324 + -324 + -38x + x2 = 0 + -324

Combine like terms: 324 + -324 = 0
0 + -38x + x2 = 0 + -324
-38x + x2 = 0 + -324

Combine like terms: 0 + -324 = -324
-38x + x2 = -324

The x term is -38x.  Take half its coefficient (-19).
Square it (361) and add it to both sides.

Add '361' to each side of the equation.
-38x + 361 + x2 = -324 + 361

Reorder the terms:
361 + -38x + x2 = -324 + 361

Combine like terms: -324 + 361 = 37
361 + -38x + x2 = 37

Factor a perfect square on the left side:
(x + -19)(x + -19) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(x + -19) equal to 6.08276253 and -6.08276253.


Subproblem 1
x + -19 = 6.08276253

Simplifying
x + -19 = 6.08276253

Reorder the terms:
-19 + x = 6.08276253

Solving
-19 + x = 6.08276253

Solving for variable 'x'.

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

Add '19' to each side of the equation.
-19 + 19 + x = 6.08276253 + 19

Combine like terms: -19 + 19 = 0
0 + x = 6.08276253 + 19
x = 6.08276253 + 19

Combine like terms: 6.08276253 + 19 = 25.08276253
x = 25.08276253

Simplifying
x = 25.08276253


Subproblem 2
x + -19 = -6.08276253

Simplifying
x + -19 = -6.08276253

Reorder the terms:
-19 + x = -6.08276253

Solving
-19 + x = -6.08276253

Solving for variable 'x'.

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

Add '19' to each side of the equation.
-19 + 19 + x = -6.08276253 + 19

Combine like terms: -19 + 19 = 0
0 + x = -6.08276253 + 19
x = -6.08276253 + 19

Combine like terms: -6.08276253 + 19 = 12.91723747
x = 12.91723747

Simplifying
x = 12.91723747


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.08276253, 12.91723747}

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