a^2+7a-10=-5a+4a

Solution for a^2+7a-10=-5a+4a equation:

Simplifying
a2 + 7a + -10 = -5a + 4a

Reorder the terms:
-10 + 7a + a2 = -5a + 4a

Combine like terms: -5a + 4a = -1a
-10 + 7a + a2 = -1a

Solving
-10 + 7a + a2 = -1a

Solving for variable 'a'.

Reorder the terms:
-10 + 7a + a + a2 = -1a + a

Combine like terms: 7a + a = 8a
-10 + 8a + a2 = -1a + a

Combine like terms: -1a + a = 0
-10 + 8a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 8a + 10 + a2 = 0 + 10

Reorder the terms:
-10 + 10 + 8a + a2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 8a + a2 = 0 + 10
8a + a2 = 0 + 10

Combine like terms: 0 + 10 = 10
8a + a2 = 10

The a term is 8a.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8a + 16 + a2 = 10 + 16

Reorder the terms:
16 + 8a + a2 = 10 + 16

Combine like terms: 10 + 16 = 26
16 + 8a + a2 = 26

Factor a perfect square on the left side:
(a + 4)(a + 4) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(a + 4) equal to 5.099019514 and -5.099019514.

Subproblem 1
a + 4 = 5.099019514

Simplifying
a + 4 = 5.099019514

Reorder the terms:
4 + a = 5.099019514

Solving
4 + a = 5.099019514

Solving for variable 'a'.

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

Add '-4' to each side of the equation.
4 + -4 + a = 5.099019514 + -4

Combine like terms: 4 + -4 = 0
0 + a = 5.099019514 + -4
a = 5.099019514 + -4

Combine like terms: 5.099019514 + -4 = 1.099019514
a = 1.099019514

Simplifying
a = 1.099019514

Subproblem 2
a + 4 = -5.099019514

Simplifying
a + 4 = -5.099019514

Reorder the terms:
4 + a = -5.099019514

Solving
4 + a = -5.099019514

Solving for variable 'a'.

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

Add '-4' to each side of the equation.
4 + -4 + a = -5.099019514 + -4

Combine like terms: 4 + -4 = 0
0 + a = -5.099019514 + -4
a = -5.099019514 + -4

Combine like terms: -5.099019514 + -4 = -9.099019514
a = -9.099019514

Simplifying
a = -9.099019514

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.099019514, -9.099019514}