4a^2-16a+74=4

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Solution for 4a^2-16a+74=4 equation: 


Simplifying
4a2 + -16a + 74 = 4

Reorder the terms:
74 + -16a + 4a2 = 4

Solving
74 + -16a + 4a2 = 4

Solving for variable 'a'.

Reorder the terms:
74 + -4 + -16a + 4a2 = 4 + -4

Combine like terms: 74 + -4 = 70
70 + -16a + 4a2 = 4 + -4

Combine like terms: 4 + -4 = 0
70 + -16a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(35 + -8a + 2a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(35 + -8a + 2a2)' equal to zero and attempt to solve:

Simplifying
35 + -8a + 2a2 = 0

Solving
35 + -8a + 2a2 = 0

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

Divide each side by '2'.
17.5 + -4a + a2 = 0

Move the constant term to the right:

Add '-17.5' to each side of the equation.
17.5 + -4a + -17.5 + a2 = 0 + -17.5

Reorder the terms:
17.5 + -17.5 + -4a + a2 = 0 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + -4a + a2 = 0 + -17.5
-4a + a2 = 0 + -17.5

Combine like terms: 0 + -17.5 = -17.5
-4a + a2 = -17.5

The a term is -4a.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4a + 4 + a2 = -17.5 + 4

Reorder the terms:
4 + -4a + a2 = -17.5 + 4

Combine like terms: -17.5 + 4 = -13.5
4 + -4a + a2 = -13.5

Factor a perfect square on the left side:
(a + -2)(a + -2) = -13.5

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.

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