a^2-24a+9=0

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Solution for a^2-24a+9=0 equation: 


Simplifying
a2 + -24a + 9 = 0

Reorder the terms:
9 + -24a + a2 = 0

Solving
9 + -24a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -24a + -9 + a2 = 0 + -9

Reorder the terms:
9 + -9 + -24a + a2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -24a + a2 = 0 + -9
-24a + a2 = 0 + -9

Combine like terms: 0 + -9 = -9
-24a + a2 = -9

The a term is -24a.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24a + 144 + a2 = -9 + 144

Reorder the terms:
144 + -24a + a2 = -9 + 144

Combine like terms: -9 + 144 = 135
144 + -24a + a2 = 135

Factor a perfect square on the left side:
(a + -12)(a + -12) = 135

Calculate the square root of the right side: 11.618950039

Break this problem into two subproblems by setting 
(a + -12) equal to 11.618950039 and -11.618950039.


Subproblem 1
a + -12 = 11.618950039

Simplifying
a + -12 = 11.618950039

Reorder the terms:
-12 + a = 11.618950039

Solving
-12 + a = 11.618950039

Solving for variable 'a'.

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

Add '12' to each side of the equation.
-12 + 12 + a = 11.618950039 + 12

Combine like terms: -12 + 12 = 0
0 + a = 11.618950039 + 12
a = 11.618950039 + 12

Combine like terms: 11.618950039 + 12 = 23.618950039
a = 23.618950039

Simplifying
a = 23.618950039


Subproblem 2
a + -12 = -11.618950039

Simplifying
a + -12 = -11.618950039

Reorder the terms:
-12 + a = -11.618950039

Solving
-12 + a = -11.618950039

Solving for variable 'a'.

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

Add '12' to each side of the equation.
-12 + 12 + a = -11.618950039 + 12

Combine like terms: -12 + 12 = 0
0 + a = -11.618950039 + 12
a = -11.618950039 + 12

Combine like terms: -11.618950039 + 12 = 0.381049961
a = 0.381049961

Simplifying
a = 0.381049961


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {23.618950039, 0.381049961}

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