x^2-30x-39=0

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Solution for x^2-30x-39=0 equation: 


Simplifying
x2 + -30x + -39 = 0

Reorder the terms:
-39 + -30x + x2 = 0

Solving
-39 + -30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + -30x + 39 + x2 = 0 + 39

Reorder the terms:
-39 + 39 + -30x + x2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + -30x + x2 = 0 + 39
-30x + x2 = 0 + 39

Combine like terms: 0 + 39 = 39
-30x + x2 = 39

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = 39 + 225

Reorder the terms:
225 + -30x + x2 = 39 + 225

Combine like terms: 39 + 225 = 264
225 + -30x + x2 = 264

Factor a perfect square on the left side:
(x + -15)(x + -15) = 264

Calculate the square root of the right side: 16.248076809

Break this problem into two subproblems by setting 
(x + -15) equal to 16.248076809 and -16.248076809.


Subproblem 1
x + -15 = 16.248076809

Simplifying
x + -15 = 16.248076809

Reorder the terms:
-15 + x = 16.248076809

Solving
-15 + x = 16.248076809

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 16.248076809 + 15

Combine like terms: -15 + 15 = 0
0 + x = 16.248076809 + 15
x = 16.248076809 + 15

Combine like terms: 16.248076809 + 15 = 31.248076809
x = 31.248076809

Simplifying
x = 31.248076809


Subproblem 2
x + -15 = -16.248076809

Simplifying
x + -15 = -16.248076809

Reorder the terms:
-15 + x = -16.248076809

Solving
-15 + x = -16.248076809

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -16.248076809 + 15

Combine like terms: -15 + 15 = 0
0 + x = -16.248076809 + 15
x = -16.248076809 + 15

Combine like terms: -16.248076809 + 15 = -1.248076809
x = -1.248076809

Simplifying
x = -1.248076809


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {31.248076809, -1.248076809}

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