2a^2-20a+16=0

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Solution for 2a^2-20a+16=0 equation: 


Simplifying
2a2 + -20a + 16 = 0

Reorder the terms:
16 + -20a + 2a2 = 0

Solving
16 + -20a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -10a + a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -10a + a2)' equal to zero and attempt to solve:

Simplifying
8 + -10a + a2 = 0

Solving
8 + -10a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -10a + -8 + a2 = 0 + -8

Reorder the terms:
8 + -8 + -10a + a2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -10a + a2 = 0 + -8
-10a + a2 = 0 + -8

Combine like terms: 0 + -8 = -8
-10a + a2 = -8

The a term is -10a.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10a + 25 + a2 = -8 + 25

Reorder the terms:
25 + -10a + a2 = -8 + 25

Combine like terms: -8 + 25 = 17
25 + -10a + a2 = 17

Factor a perfect square on the left side:
(a + -5)(a + -5) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(a + -5) equal to 4.123105626 and -4.123105626.


Subproblem 1
a + -5 = 4.123105626

Simplifying
a + -5 = 4.123105626

Reorder the terms:
-5 + a = 4.123105626

Solving
-5 + a = 4.123105626

Solving for variable 'a'.

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

Add '5' to each side of the equation.
-5 + 5 + a = 4.123105626 + 5

Combine like terms: -5 + 5 = 0
0 + a = 4.123105626 + 5
a = 4.123105626 + 5

Combine like terms: 4.123105626 + 5 = 9.123105626
a = 9.123105626

Simplifying
a = 9.123105626


Subproblem 2
a + -5 = -4.123105626

Simplifying
a + -5 = -4.123105626

Reorder the terms:
-5 + a = -4.123105626

Solving
-5 + a = -4.123105626

Solving for variable 'a'.

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

Add '5' to each side of the equation.
-5 + 5 + a = -4.123105626 + 5

Combine like terms: -5 + 5 = 0
0 + a = -4.123105626 + 5
a = -4.123105626 + 5

Combine like terms: -4.123105626 + 5 = 0.876894374
a = 0.876894374

Simplifying
a = 0.876894374


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {9.123105626, 0.876894374}
Solution
a = {9.123105626, 0.876894374}

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