x^2-38x-325=0

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Solution for x^2-38x-325=0 equation: 


Simplifying
x2 + -38x + -325 = 0

Reorder the terms:
-325 + -38x + x2 = 0

Solving
-325 + -38x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '325' to each side of the equation.
-325 + -38x + 325 + x2 = 0 + 325

Reorder the terms:
-325 + 325 + -38x + x2 = 0 + 325

Combine like terms: -325 + 325 = 0
0 + -38x + x2 = 0 + 325
-38x + x2 = 0 + 325

Combine like terms: 0 + 325 = 325
-38x + x2 = 325

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 = 325 + 361

Reorder the terms:
361 + -38x + x2 = 325 + 361

Combine like terms: 325 + 361 = 686
361 + -38x + x2 = 686

Factor a perfect square on the left side:
(x + -19)(x + -19) = 686

Calculate the square root of the right side: 26.191601707

Break this problem into two subproblems by setting 
(x + -19) equal to 26.191601707 and -26.191601707.


Subproblem 1
x + -19 = 26.191601707

Simplifying
x + -19 = 26.191601707

Reorder the terms:
-19 + x = 26.191601707

Solving
-19 + x = 26.191601707

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 = 26.191601707 + 19

Combine like terms: -19 + 19 = 0
0 + x = 26.191601707 + 19
x = 26.191601707 + 19

Combine like terms: 26.191601707 + 19 = 45.191601707
x = 45.191601707

Simplifying
x = 45.191601707


Subproblem 2
x + -19 = -26.191601707

Simplifying
x + -19 = -26.191601707

Reorder the terms:
-19 + x = -26.191601707

Solving
-19 + x = -26.191601707

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 = -26.191601707 + 19

Combine like terms: -19 + 19 = 0
0 + x = -26.191601707 + 19
x = -26.191601707 + 19

Combine like terms: -26.191601707 + 19 = -7.191601707
x = -7.191601707

Simplifying
x = -7.191601707


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {45.191601707, -7.191601707}

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