7a^2-77a+26=

Solution for 7a^2-77a+26= equation:

Simplifying
7a2 + -77a + 26 = 0

Reorder the terms:
26 + -77a + 7a2 = 0

Solving
26 + -77a + 7a2 = 0

Solving for variable 'a'.

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

Divide each side by '7'.
3.714285714 + -11a + a2 = 0

Move the constant term to the right:

Add '-3.714285714' to each side of the equation.
3.714285714 + -11a + -3.714285714 + a2 = 0 + -3.714285714

Reorder the terms:
3.714285714 + -3.714285714 + -11a + a2 = 0 + -3.714285714

Combine like terms: 3.714285714 + -3.714285714 = 0.000000000
0.000000000 + -11a + a2 = 0 + -3.714285714
-11a + a2 = 0 + -3.714285714

Combine like terms: 0 + -3.714285714 = -3.714285714
-11a + a2 = -3.714285714

The a term is -11a.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11a + 30.25 + a2 = -3.714285714 + 30.25

Reorder the terms:
30.25 + -11a + a2 = -3.714285714 + 30.25

Combine like terms: -3.714285714 + 30.25 = 26.535714286
30.25 + -11a + a2 = 26.535714286

Factor a perfect square on the left side:
(a + -5.5)(a + -5.5) = 26.535714286

Calculate the square root of the right side: 5.151282781

Break this problem into two subproblems by setting 
(a + -5.5) equal to 5.151282781 and -5.151282781.

Subproblem 1
a + -5.5 = 5.151282781

Simplifying
a + -5.5 = 5.151282781

Reorder the terms:
-5.5 + a = 5.151282781

Solving
-5.5 + a = 5.151282781

Solving for variable 'a'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + a = 5.151282781 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + a = 5.151282781 + 5.5
a = 5.151282781 + 5.5

Combine like terms: 5.151282781 + 5.5 = 10.651282781
a = 10.651282781

Simplifying
a = 10.651282781

Subproblem 2
a + -5.5 = -5.151282781

Simplifying
a + -5.5 = -5.151282781

Reorder the terms:
-5.5 + a = -5.151282781

Solving
-5.5 + a = -5.151282781

Solving for variable 'a'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + a = -5.151282781 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + a = -5.151282781 + 5.5
a = -5.151282781 + 5.5

Combine like terms: -5.151282781 + 5.5 = 0.348717219
a = 0.348717219

Simplifying
a = 0.348717219

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {10.651282781, 0.348717219}