a^2-16a+21=0

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Solution for a^2-16a+21=0 equation: 


Simplifying
a2 + -16a + 21 = 0

Reorder the terms:
21 + -16a + a2 = 0

Solving
21 + -16a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -16a + -21 + a2 = 0 + -21

Reorder the terms:
21 + -21 + -16a + a2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -16a + a2 = 0 + -21
-16a + a2 = 0 + -21

Combine like terms: 0 + -21 = -21
-16a + a2 = -21

The a term is -16a.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16a + 64 + a2 = -21 + 64

Reorder the terms:
64 + -16a + a2 = -21 + 64

Combine like terms: -21 + 64 = 43
64 + -16a + a2 = 43

Factor a perfect square on the left side:
(a + -8)(a + -8) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(a + -8) equal to 6.557438524 and -6.557438524.


Subproblem 1
a + -8 = 6.557438524

Simplifying
a + -8 = 6.557438524

Reorder the terms:
-8 + a = 6.557438524

Solving
-8 + a = 6.557438524

Solving for variable 'a'.

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

Add '8' to each side of the equation.
-8 + 8 + a = 6.557438524 + 8

Combine like terms: -8 + 8 = 0
0 + a = 6.557438524 + 8
a = 6.557438524 + 8

Combine like terms: 6.557438524 + 8 = 14.557438524
a = 14.557438524

Simplifying
a = 14.557438524


Subproblem 2
a + -8 = -6.557438524

Simplifying
a + -8 = -6.557438524

Reorder the terms:
-8 + a = -6.557438524

Solving
-8 + a = -6.557438524

Solving for variable 'a'.

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

Add '8' to each side of the equation.
-8 + 8 + a = -6.557438524 + 8

Combine like terms: -8 + 8 = 0
0 + a = -6.557438524 + 8
a = -6.557438524 + 8

Combine like terms: -6.557438524 + 8 = 1.442561476
a = 1.442561476

Simplifying
a = 1.442561476


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {14.557438524, 1.442561476}

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