2a^2+a-1=10

Solution for 2a^2+a-1=10 equation:

Simplifying
2a2 + a + -1 = 10

Reorder the terms:
-1 + a + 2a2 = 10

Solving
-1 + a + 2a2 = 10

Solving for variable 'a'.

Reorder the terms:
-1 + -10 + a + 2a2 = 10 + -10

Combine like terms: -1 + -10 = -11
-11 + a + 2a2 = 10 + -10

Combine like terms: 10 + -10 = 0
-11 + a + 2a2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-5.5 + 0.5a + a2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + 0.5a + 5.5 + a2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + 0.5a + a2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + 0.5a + a2 = 0 + 5.5
0.5a + a2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
0.5a + a2 = 5.5

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5a + 0.25 + a2 = 5.5 + 0.25

Reorder the terms:
0.25 + 0.5a + a2 = 5.5 + 0.25

Combine like terms: 5.5 + 0.25 = 5.75
0.25 + 0.5a + a2 = 5.75

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(a + 0.5) equal to 2.397915762 and -2.397915762.

Subproblem 1
a + 0.5 = 2.397915762

Simplifying
a + 0.5 = 2.397915762

Reorder the terms:
0.5 + a = 2.397915762

Solving
0.5 + a = 2.397915762

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = 2.397915762 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = 2.397915762 + -0.5
a = 2.397915762 + -0.5

Combine like terms: 2.397915762 + -0.5 = 1.897915762
a = 1.897915762

Simplifying
a = 1.897915762

Subproblem 2
a + 0.5 = -2.397915762

Simplifying
a + 0.5 = -2.397915762

Reorder the terms:
0.5 + a = -2.397915762

Solving
0.5 + a = -2.397915762

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = -2.397915762 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = -2.397915762 + -0.5
a = -2.397915762 + -0.5

Combine like terms: -2.397915762 + -0.5 = -2.897915762
a = -2.897915762

Simplifying
a = -2.897915762

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.897915762, -2.897915762}