x^2-17x-210=0

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Solution for x^2-17x-210=0 equation: 


Simplifying
x2 + -17x + -210 = 0

Reorder the terms:
-210 + -17x + x2 = 0

Solving
-210 + -17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '210' to each side of the equation.
-210 + -17x + 210 + x2 = 0 + 210

Reorder the terms:
-210 + 210 + -17x + x2 = 0 + 210

Combine like terms: -210 + 210 = 0
0 + -17x + x2 = 0 + 210
-17x + x2 = 0 + 210

Combine like terms: 0 + 210 = 210
-17x + x2 = 210

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 = 210 + 72.25

Reorder the terms:
72.25 + -17x + x2 = 210 + 72.25

Combine like terms: 210 + 72.25 = 282.25
72.25 + -17x + x2 = 282.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 282.25

Calculate the square root of the right side: 16.800297616

Break this problem into two subproblems by setting 
(x + -8.5) equal to 16.800297616 and -16.800297616.


Subproblem 1
x + -8.5 = 16.800297616

Simplifying
x + -8.5 = 16.800297616

Reorder the terms:
-8.5 + x = 16.800297616

Solving
-8.5 + x = 16.800297616

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 = 16.800297616 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = 16.800297616 + 8.5
x = 16.800297616 + 8.5

Combine like terms: 16.800297616 + 8.5 = 25.300297616
x = 25.300297616

Simplifying
x = 25.300297616


Subproblem 2
x + -8.5 = -16.800297616

Simplifying
x + -8.5 = -16.800297616

Reorder the terms:
-8.5 + x = -16.800297616

Solving
-8.5 + x = -16.800297616

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 = -16.800297616 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = -16.800297616 + 8.5
x = -16.800297616 + 8.5

Combine like terms: -16.800297616 + 8.5 = -8.300297616
x = -8.300297616

Simplifying
x = -8.300297616


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.300297616, -8.300297616}

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