x^2-17x-625=0

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Solution for x^2-17x-625=0 equation: 


Simplifying
x2 + -17x + -625 = 0

Reorder the terms:
-625 + -17x + x2 = 0

Solving
-625 + -17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '625' to each side of the equation.
-625 + -17x + 625 + x2 = 0 + 625

Reorder the terms:
-625 + 625 + -17x + x2 = 0 + 625

Combine like terms: -625 + 625 = 0
0 + -17x + x2 = 0 + 625
-17x + x2 = 0 + 625

Combine like terms: 0 + 625 = 625
-17x + x2 = 625

The x term is -17x.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x + 72.25 + x2 = 625 + 72.25

Reorder the terms:
72.25 + -17x + x2 = 625 + 72.25

Combine like terms: 625 + 72.25 = 697.25
72.25 + -17x + x2 = 697.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 697.25

Calculate the square root of the right side: 26.405491853

Break this problem into two subproblems by setting 
(x + -8.5) equal to 26.405491853 and -26.405491853.


Subproblem 1
x + -8.5 = 26.405491853

Simplifying
x + -8.5 = 26.405491853

Reorder the terms:
-8.5 + x = 26.405491853

Solving
-8.5 + x = 26.405491853

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = 26.405491853 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = 26.405491853 + 8.5
x = 26.405491853 + 8.5

Combine like terms: 26.405491853 + 8.5 = 34.905491853
x = 34.905491853

Simplifying
x = 34.905491853


Subproblem 2
x + -8.5 = -26.405491853

Simplifying
x + -8.5 = -26.405491853

Reorder the terms:
-8.5 + x = -26.405491853

Solving
-8.5 + x = -26.405491853

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = -26.405491853 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = -26.405491853 + 8.5
x = -26.405491853 + 8.5

Combine like terms: -26.405491853 + 8.5 = -17.905491853
x = -17.905491853

Simplifying
x = -17.905491853


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {34.905491853, -17.905491853}

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