x^2-6x-25=0

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Solution for x^2-6x-25=0 equation: 


Simplifying
x2 + -6x + -25 = 0

Reorder the terms:
-25 + -6x + x2 = 0

Solving
-25 + -6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -6x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -6x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -6x + x2 = 0 + 25
-6x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-6x + x2 = 25

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 = 25 + 9

Reorder the terms:
9 + -6x + x2 = 25 + 9

Combine like terms: 25 + 9 = 34
9 + -6x + x2 = 34

Factor a perfect square on the left side:
(x + -3)(x + -3) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(x + -3) equal to 5.830951895 and -5.830951895.


Subproblem 1
x + -3 = 5.830951895

Simplifying
x + -3 = 5.830951895

Reorder the terms:
-3 + x = 5.830951895

Solving
-3 + x = 5.830951895

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 = 5.830951895 + 3

Combine like terms: -3 + 3 = 0
0 + x = 5.830951895 + 3
x = 5.830951895 + 3

Combine like terms: 5.830951895 + 3 = 8.830951895
x = 8.830951895

Simplifying
x = 8.830951895


Subproblem 2
x + -3 = -5.830951895

Simplifying
x + -3 = -5.830951895

Reorder the terms:
-3 + x = -5.830951895

Solving
-3 + x = -5.830951895

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 = -5.830951895 + 3

Combine like terms: -3 + 3 = 0
0 + x = -5.830951895 + 3
x = -5.830951895 + 3

Combine like terms: -5.830951895 + 3 = -2.830951895
x = -2.830951895

Simplifying
x = -2.830951895


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.830951895, -2.830951895}

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