x^2-6x-30=0

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Solution for x^2-6x-30=0 equation: 


Simplifying
x2 + -6x + -30 = 0

Reorder the terms:
-30 + -6x + x2 = 0

Solving
-30 + -6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -6x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -6x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -6x + x2 = 0 + 30
-6x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-6x + x2 = 30

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 30 + 9

Reorder the terms:
9 + -6x + x2 = 30 + 9

Combine like terms: 30 + 9 = 39
9 + -6x + x2 = 39

Factor a perfect square on the left side:
(x + -3)(x + -3) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(x + -3) equal to 6.244997998 and -6.244997998.


Subproblem 1
x + -3 = 6.244997998

Simplifying
x + -3 = 6.244997998

Reorder the terms:
-3 + x = 6.244997998

Solving
-3 + x = 6.244997998

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 6.244997998 + 3

Combine like terms: -3 + 3 = 0
0 + x = 6.244997998 + 3
x = 6.244997998 + 3

Combine like terms: 6.244997998 + 3 = 9.244997998
x = 9.244997998

Simplifying
x = 9.244997998


Subproblem 2
x + -3 = -6.244997998

Simplifying
x + -3 = -6.244997998

Reorder the terms:
-3 + x = -6.244997998

Solving
-3 + x = -6.244997998

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -6.244997998 + 3

Combine like terms: -3 + 3 = 0
0 + x = -6.244997998 + 3
x = -6.244997998 + 3

Combine like terms: -6.244997998 + 3 = -3.244997998
x = -3.244997998

Simplifying
x = -3.244997998


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.244997998, -3.244997998}

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