x^2-17x-25=0

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Solution for x^2-17x-25=0 equation: 


Simplifying
x2 + -17x + -25 = 0

Reorder the terms:
-25 + -17x + x2 = 0

Solving
-25 + -17x + 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 + -17x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -17x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -17x + x2 = 0 + 25
-17x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-17x + x2 = 25

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 = 25 + 72.25

Reorder the terms:
72.25 + -17x + x2 = 25 + 72.25

Combine like terms: 25 + 72.25 = 97.25
72.25 + -17x + x2 = 97.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 97.25

Calculate the square root of the right side: 9.861541462

Break this problem into two subproblems by setting 
(x + -8.5) equal to 9.861541462 and -9.861541462.


Subproblem 1
x + -8.5 = 9.861541462

Simplifying
x + -8.5 = 9.861541462

Reorder the terms:
-8.5 + x = 9.861541462

Solving
-8.5 + x = 9.861541462

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 = 9.861541462 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = 9.861541462 + 8.5
x = 9.861541462 + 8.5

Combine like terms: 9.861541462 + 8.5 = 18.361541462
x = 18.361541462

Simplifying
x = 18.361541462


Subproblem 2
x + -8.5 = -9.861541462

Simplifying
x + -8.5 = -9.861541462

Reorder the terms:
-8.5 + x = -9.861541462

Solving
-8.5 + x = -9.861541462

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 = -9.861541462 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = -9.861541462 + 8.5
x = -9.861541462 + 8.5

Combine like terms: -9.861541462 + 8.5 = -1.361541462
x = -1.361541462

Simplifying
x = -1.361541462


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.361541462, -1.361541462}

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