a^2-8a+10a=31-5a

Solution for a^2-8a+10a=31-5a equation:

Simplifying
a2 + -8a + 10a = 31 + -5a

Reorder the terms:
-8a + 10a + a2 = 31 + -5a

Combine like terms: -8a + 10a = 2a
2a + a2 = 31 + -5a

Solving
2a + a2 = 31 + -5a

Solving for variable 'a'.

Reorder the terms:
-31 + 2a + 5a + a2 = 31 + -5a + -31 + 5a

Combine like terms: 2a + 5a = 7a
-31 + 7a + a2 = 31 + -5a + -31 + 5a

Reorder the terms:
-31 + 7a + a2 = 31 + -31 + -5a + 5a

Combine like terms: 31 + -31 = 0
-31 + 7a + a2 = 0 + -5a + 5a
-31 + 7a + a2 = -5a + 5a

Combine like terms: -5a + 5a = 0
-31 + 7a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 7a + 31 + a2 = 0 + 31

Reorder the terms:
-31 + 31 + 7a + a2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 7a + a2 = 0 + 31
7a + a2 = 0 + 31

Combine like terms: 0 + 31 = 31
7a + a2 = 31

The a term is 7a.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7a + 12.25 + a2 = 31 + 12.25

Reorder the terms:
12.25 + 7a + a2 = 31 + 12.25

Combine like terms: 31 + 12.25 = 43.25
12.25 + 7a + a2 = 43.25

Factor a perfect square on the left side:
(a + 3.5)(a + 3.5) = 43.25

Calculate the square root of the right side: 6.576473219

Break this problem into two subproblems by setting 
(a + 3.5) equal to 6.576473219 and -6.576473219.

Subproblem 1
a + 3.5 = 6.576473219

Simplifying
a + 3.5 = 6.576473219

Reorder the terms:
3.5 + a = 6.576473219

Solving
3.5 + a = 6.576473219

Solving for variable 'a'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + a = 6.576473219 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + a = 6.576473219 + -3.5
a = 6.576473219 + -3.5

Combine like terms: 6.576473219 + -3.5 = 3.076473219
a = 3.076473219

Simplifying
a = 3.076473219

Subproblem 2
a + 3.5 = -6.576473219

Simplifying
a + 3.5 = -6.576473219

Reorder the terms:
3.5 + a = -6.576473219

Solving
3.5 + a = -6.576473219

Solving for variable 'a'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + a = -6.576473219 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + a = -6.576473219 + -3.5
a = -6.576473219 + -3.5

Combine like terms: -6.576473219 + -3.5 = -10.076473219
a = -10.076473219

Simplifying
a = -10.076473219

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.076473219, -10.076473219}