a^2+7a-10=0

Solution for a^2+7a-10=0 equation:

Simplifying
a2 + 7a + -10 = 0

Reorder the terms:
-10 + 7a + a2 = 0

Solving
-10 + 7a + 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 + 7a + 10 + a2 = 0 + 10

Reorder the terms:
-10 + 10 + 7a + a2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 7a + a2 = 0 + 10
7a + a2 = 0 + 10

Combine like terms: 0 + 10 = 10
7a + a2 = 10

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 = 10 + 12.25

Reorder the terms:
12.25 + 7a + a2 = 10 + 12.25

Combine like terms: 10 + 12.25 = 22.25
12.25 + 7a + a2 = 22.25

Factor a perfect square on the left side:
(a + 3.5)(a + 3.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(a + 3.5) equal to 4.716990566 and -4.716990566.

Subproblem 1
a + 3.5 = 4.716990566

Simplifying
a + 3.5 = 4.716990566

Reorder the terms:
3.5 + a = 4.716990566

Solving
3.5 + a = 4.716990566

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 = 4.716990566 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + a = 4.716990566 + -3.5
a = 4.716990566 + -3.5

Combine like terms: 4.716990566 + -3.5 = 1.216990566
a = 1.216990566

Simplifying
a = 1.216990566

Subproblem 2
a + 3.5 = -4.716990566

Simplifying
a + 3.5 = -4.716990566

Reorder the terms:
3.5 + a = -4.716990566

Solving
3.5 + a = -4.716990566

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 = -4.716990566 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + a = -4.716990566 + -3.5
a = -4.716990566 + -3.5

Combine like terms: -4.716990566 + -3.5 = -8.216990566
a = -8.216990566

Simplifying
a = -8.216990566

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.216990566, -8.216990566}