a^2-5a-9=0

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Solution for a^2-5a-9=0 equation: 


Simplifying
a2 + -5a + -9 = 0

Reorder the terms:
-9 + -5a + a2 = 0

Solving
-9 + -5a + 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 + -5a + 9 + a2 = 0 + 9

Reorder the terms:
-9 + 9 + -5a + a2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -5a + a2 = 0 + 9
-5a + a2 = 0 + 9

Combine like terms: 0 + 9 = 9
-5a + a2 = 9

The a term is -5a.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5a + 6.25 + a2 = 9 + 6.25

Reorder the terms:
6.25 + -5a + a2 = 9 + 6.25

Combine like terms: 9 + 6.25 = 15.25
6.25 + -5a + a2 = 15.25

Factor a perfect square on the left side:
(a + -2.5)(a + -2.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(a + -2.5) equal to 3.905124838 and -3.905124838.


Subproblem 1
a + -2.5 = 3.905124838

Simplifying
a + -2.5 = 3.905124838

Reorder the terms:
-2.5 + a = 3.905124838

Solving
-2.5 + a = 3.905124838

Solving for variable 'a'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + a = 3.905124838 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + a = 3.905124838 + 2.5
a = 3.905124838 + 2.5

Combine like terms: 3.905124838 + 2.5 = 6.405124838
a = 6.405124838

Simplifying
a = 6.405124838


Subproblem 2
a + -2.5 = -3.905124838

Simplifying
a + -2.5 = -3.905124838

Reorder the terms:
-2.5 + a = -3.905124838

Solving
-2.5 + a = -3.905124838

Solving for variable 'a'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + a = -3.905124838 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + a = -3.905124838 + 2.5
a = -3.905124838 + 2.5

Combine like terms: -3.905124838 + 2.5 = -1.405124838
a = -1.405124838

Simplifying
a = -1.405124838


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {6.405124838, -1.405124838}

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