a^2-2a=17

Solution for a^2-2a=17 equation:

Simplifying
a2 + -2a = 17

Reorder the terms:
-2a + a2 = 17

Solving
-2a + a2 = 17

Solving for variable 'a'.

Reorder the terms:
-17 + -2a + a2 = 17 + -17

Combine like terms: 17 + -17 = 0
-17 + -2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -2a + 17 + a2 = 0 + 17

Reorder the terms:
-17 + 17 + -2a + a2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -2a + a2 = 0 + 17
-2a + a2 = 0 + 17

Combine like terms: 0 + 17 = 17
-2a + a2 = 17

The a term is -2a.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2a + 1 + a2 = 17 + 1

Reorder the terms:
1 + -2a + a2 = 17 + 1

Combine like terms: 17 + 1 = 18
1 + -2a + a2 = 18

Factor a perfect square on the left side:
(a + -1)(a + -1) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(a + -1) equal to 4.242640687 and -4.242640687.

Subproblem 1
a + -1 = 4.242640687

Simplifying
a + -1 = 4.242640687

Reorder the terms:
-1 + a = 4.242640687

Solving
-1 + a = 4.242640687

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a = 4.242640687 + 1

Combine like terms: -1 + 1 = 0
0 + a = 4.242640687 + 1
a = 4.242640687 + 1

Combine like terms: 4.242640687 + 1 = 5.242640687
a = 5.242640687

Simplifying
a = 5.242640687

Subproblem 2
a + -1 = -4.242640687

Simplifying
a + -1 = -4.242640687

Reorder the terms:
-1 + a = -4.242640687

Solving
-1 + a = -4.242640687

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a = -4.242640687 + 1

Combine like terms: -1 + 1 = 0
0 + a = -4.242640687 + 1
a = -4.242640687 + 1

Combine like terms: -4.242640687 + 1 = -3.242640687
a = -3.242640687

Simplifying
a = -3.242640687

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {5.242640687, -3.242640687}