2a^2-7a+2=0

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

Simplifying
2a2 + -7a + 2 = 0

Reorder the terms:
2 + -7a + 2a2 = 0

Solving
2 + -7a + 2a2 = 0

Solving for variable 'a'.

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

Divide each side by '2'.
1 + -3.5a + a2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3.5a + -1 + a2 = 0 + -1

Reorder the terms:
1 + -1 + -3.5a + a2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3.5a + a2 = 0 + -1
-3.5a + a2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3.5a + a2 = -1

The a term is -3.5a.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5a + 3.0625 + a2 = -1 + 3.0625

Reorder the terms:
3.0625 + -3.5a + a2 = -1 + 3.0625

Combine like terms: -1 + 3.0625 = 2.0625
3.0625 + -3.5a + a2 = 2.0625

Factor a perfect square on the left side:
(a + -1.75)(a + -1.75) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(a + -1.75) equal to 1.436140662 and -1.436140662.

Subproblem 1
a + -1.75 = 1.436140662

Simplifying
a + -1.75 = 1.436140662

Reorder the terms:
-1.75 + a = 1.436140662

Solving
-1.75 + a = 1.436140662

Solving for variable 'a'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + a = 1.436140662 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + a = 1.436140662 + 1.75
a = 1.436140662 + 1.75

Combine like terms: 1.436140662 + 1.75 = 3.186140662
a = 3.186140662

Simplifying
a = 3.186140662

Subproblem 2
a + -1.75 = -1.436140662

Simplifying
a + -1.75 = -1.436140662

Reorder the terms:
-1.75 + a = -1.436140662

Solving
-1.75 + a = -1.436140662

Solving for variable 'a'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + a = -1.436140662 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + a = -1.436140662 + 1.75
a = -1.436140662 + 1.75

Combine like terms: -1.436140662 + 1.75 = 0.313859338
a = 0.313859338

Simplifying
a = 0.313859338

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.186140662, 0.313859338}