a^2+6a-10=0

Solution for a^2+6a-10=0 equation:

Simplifying
a2 + 6a + -10 = 0

Reorder the terms:
-10 + 6a + a2 = 0

Solving
-10 + 6a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 6a + 10 + a2 = 0 + 10

Reorder the terms:
-10 + 10 + 6a + a2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 6a + a2 = 0 + 10
6a + a2 = 0 + 10

Combine like terms: 0 + 10 = 10
6a + a2 = 10

The a term is 6a.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6a + 9 + a2 = 10 + 9

Reorder the terms:
9 + 6a + a2 = 10 + 9

Combine like terms: 10 + 9 = 19
9 + 6a + a2 = 19

Factor a perfect square on the left side:
(a + 3)(a + 3) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(a + 3) equal to 4.358898944 and -4.358898944.

Subproblem 1
a + 3 = 4.358898944

Simplifying
a + 3 = 4.358898944

Reorder the terms:
3 + a = 4.358898944

Solving
3 + a = 4.358898944

Solving for variable 'a'.

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

Add '-3' to each side of the equation.
3 + -3 + a = 4.358898944 + -3

Combine like terms: 3 + -3 = 0
0 + a = 4.358898944 + -3
a = 4.358898944 + -3

Combine like terms: 4.358898944 + -3 = 1.358898944
a = 1.358898944

Simplifying
a = 1.358898944

Subproblem 2
a + 3 = -4.358898944

Simplifying
a + 3 = -4.358898944

Reorder the terms:
3 + a = -4.358898944

Solving
3 + a = -4.358898944

Solving for variable 'a'.

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

Add '-3' to each side of the equation.
3 + -3 + a = -4.358898944 + -3

Combine like terms: 3 + -3 = 0
0 + a = -4.358898944 + -3
a = -4.358898944 + -3

Combine like terms: -4.358898944 + -3 = -7.358898944
a = -7.358898944

Simplifying
a = -7.358898944

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.358898944, -7.358898944}