-x^2+17x-5=0

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Solution for -x^2+17x-5=0 equation: 


Simplifying
-1x2 + 17x + -5 = 0

Reorder the terms:
-5 + 17x + -1x2 = 0

Solving
-5 + 17x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
5 + -17x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -17x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -17x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -17x + x2 = 0 + -5
-17x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-17x + x2 = -5

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 = -5 + 72.25

Reorder the terms:
72.25 + -17x + x2 = -5 + 72.25

Combine like terms: -5 + 72.25 = 67.25
72.25 + -17x + x2 = 67.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 67.25

Calculate the square root of the right side: 8.200609733

Break this problem into two subproblems by setting 
(x + -8.5) equal to 8.200609733 and -8.200609733.


Subproblem 1
x + -8.5 = 8.200609733

Simplifying
x + -8.5 = 8.200609733

Reorder the terms:
-8.5 + x = 8.200609733

Solving
-8.5 + x = 8.200609733

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 = 8.200609733 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = 8.200609733 + 8.5
x = 8.200609733 + 8.5

Combine like terms: 8.200609733 + 8.5 = 16.700609733
x = 16.700609733

Simplifying
x = 16.700609733


Subproblem 2
x + -8.5 = -8.200609733

Simplifying
x + -8.5 = -8.200609733

Reorder the terms:
-8.5 + x = -8.200609733

Solving
-8.5 + x = -8.200609733

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 = -8.200609733 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = -8.200609733 + 8.5
x = -8.200609733 + 8.5

Combine like terms: -8.200609733 + 8.5 = 0.299390267
x = 0.299390267

Simplifying
x = 0.299390267


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.700609733, 0.299390267}

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