x^2-17x-10=0

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Solution for x^2-17x-10=0 equation: 


Simplifying
x2 + -17x + -10 = 0

Reorder the terms:
-10 + -17x + x2 = 0

Solving
-10 + -17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -17x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -17x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -17x + x2 = 0 + 10
-17x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-17x + x2 = 10

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 = 10 + 72.25

Reorder the terms:
72.25 + -17x + x2 = 10 + 72.25

Combine like terms: 10 + 72.25 = 82.25
72.25 + -17x + x2 = 82.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 82.25

Calculate the square root of the right side: 9.069178574

Break this problem into two subproblems by setting 
(x + -8.5) equal to 9.069178574 and -9.069178574.


Subproblem 1
x + -8.5 = 9.069178574

Simplifying
x + -8.5 = 9.069178574

Reorder the terms:
-8.5 + x = 9.069178574

Solving
-8.5 + x = 9.069178574

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 = 9.069178574 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = 9.069178574 + 8.5
x = 9.069178574 + 8.5

Combine like terms: 9.069178574 + 8.5 = 17.569178574
x = 17.569178574

Simplifying
x = 17.569178574


Subproblem 2
x + -8.5 = -9.069178574

Simplifying
x + -8.5 = -9.069178574

Reorder the terms:
-8.5 + x = -9.069178574

Solving
-8.5 + x = -9.069178574

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 = -9.069178574 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = -9.069178574 + 8.5
x = -9.069178574 + 8.5

Combine like terms: -9.069178574 + 8.5 = -0.569178574
x = -0.569178574

Simplifying
x = -0.569178574


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.569178574, -0.569178574}

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