4a^2-28a+170=0

Solution for 4a^2-28a+170=0 equation:

Simplifying
4a2 + -28a + 170 = 0

Reorder the terms:
170 + -28a + 4a2 = 0

Solving
170 + -28a + 4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(85 + -14a + 2a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(85 + -14a + 2a2)' equal to zero and attempt to solve:

Simplifying
85 + -14a + 2a2 = 0

Solving
85 + -14a + 2a2 = 0

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

Divide each side by '2'.
42.5 + -7a + a2 = 0

Move the constant term to the right:

Add '-42.5' to each side of the equation.
42.5 + -7a + -42.5 + a2 = 0 + -42.5

Reorder the terms:
42.5 + -42.5 + -7a + a2 = 0 + -42.5

Combine like terms: 42.5 + -42.5 = 0.0
0.0 + -7a + a2 = 0 + -42.5
-7a + a2 = 0 + -42.5

Combine like terms: 0 + -42.5 = -42.5
-7a + a2 = -42.5

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 = -42.5 + 12.25

Reorder the terms:
12.25 + -7a + a2 = -42.5 + 12.25

Combine like terms: -42.5 + 12.25 = -30.25
12.25 + -7a + a2 = -30.25

Factor a perfect square on the left side:
(a + -3.5)(a + -3.5) = -30.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.