-2x(x+17)=13-x

Solution for -2x(x+17)=13-x equation:

Simplifying
-2x(x + 17) = 13 + -1x

Reorder the terms:
-2x(17 + x) = 13 + -1x
(17 * -2x + x * -2x) = 13 + -1x
(-34x + -2x2) = 13 + -1x

Solving
-34x + -2x2 = 13 + -1x

Solving for variable 'x'.

Reorder the terms:
-13 + -34x + x + -2x2 = 13 + -1x + -13 + x

Combine like terms: -34x + x = -33x
-13 + -33x + -2x2 = 13 + -1x + -13 + x

Reorder the terms:
-13 + -33x + -2x2 = 13 + -13 + -1x + x

Combine like terms: 13 + -13 = 0
-13 + -33x + -2x2 = 0 + -1x + x
-13 + -33x + -2x2 = -1x + x

Combine like terms: -1x + x = 0
-13 + -33x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(13 + 33x + 2x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(13 + 33x + 2x2)' equal to zero and attempt to solve:

Simplifying
13 + 33x + 2x2 = 0

Solving
13 + 33x + 2x2 = 0

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

Divide each side by '2'.
6.5 + 16.5x + x2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + 16.5x + -6.5 + x2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + 16.5x + x2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + 16.5x + x2 = 0 + -6.5
16.5x + x2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
16.5x + x2 = -6.5

The x term is 16.5x.  Take half its coefficient (8.25).
Square it (68.0625) and add it to both sides.

Add '68.0625' to each side of the equation.
16.5x + 68.0625 + x2 = -6.5 + 68.0625

Reorder the terms:
68.0625 + 16.5x + x2 = -6.5 + 68.0625

Combine like terms: -6.5 + 68.0625 = 61.5625
68.0625 + 16.5x + x2 = 61.5625

Factor a perfect square on the left side:
(x + 8.25)(x + 8.25) = 61.5625

Calculate the square root of the right side: 7.846177413

Break this problem into two subproblems by setting 
(x + 8.25) equal to 7.846177413 and -7.846177413.

Subproblem 1
x + 8.25 = 7.846177413

Simplifying
x + 8.25 = 7.846177413

Reorder the terms:
8.25 + x = 7.846177413

Solving
8.25 + x = 7.846177413

Solving for variable 'x'.

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

Add '-8.25' to each side of the equation.
8.25 + -8.25 + x = 7.846177413 + -8.25

Combine like terms: 8.25 + -8.25 = 0.00
0.00 + x = 7.846177413 + -8.25
x = 7.846177413 + -8.25

Combine like terms: 7.846177413 + -8.25 = -0.403822587
x = -0.403822587

Simplifying
x = -0.403822587

Subproblem 2
x + 8.25 = -7.846177413

Simplifying
x + 8.25 = -7.846177413

Reorder the terms:
8.25 + x = -7.846177413

Solving
8.25 + x = -7.846177413

Solving for variable 'x'.

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

Add '-8.25' to each side of the equation.
8.25 + -8.25 + x = -7.846177413 + -8.25

Combine like terms: 8.25 + -8.25 = 0.00
0.00 + x = -7.846177413 + -8.25
x = -7.846177413 + -8.25

Combine like terms: -7.846177413 + -8.25 = -16.096177413
x = -16.096177413

Simplifying
x = -16.096177413

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.403822587, -16.096177413}
Solution
x = {-0.403822587, -16.096177413}