a^2+15a-9=0

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Solution for a^2+15a-9=0 equation: 


Simplifying
a2 + 15a + -9 = 0

Reorder the terms:
-9 + 15a + a2 = 0

Solving
-9 + 15a + 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 + 15a + 9 + a2 = 0 + 9

Reorder the terms:
-9 + 9 + 15a + a2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 15a + a2 = 0 + 9
15a + a2 = 0 + 9

Combine like terms: 0 + 9 = 9
15a + a2 = 9

The a term is 15a.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15a + 56.25 + a2 = 9 + 56.25

Reorder the terms:
56.25 + 15a + a2 = 9 + 56.25

Combine like terms: 9 + 56.25 = 65.25
56.25 + 15a + a2 = 65.25

Factor a perfect square on the left side:
(a + 7.5)(a + 7.5) = 65.25

Calculate the square root of the right side: 8.077747211

Break this problem into two subproblems by setting 
(a + 7.5) equal to 8.077747211 and -8.077747211.


Subproblem 1
a + 7.5 = 8.077747211

Simplifying
a + 7.5 = 8.077747211

Reorder the terms:
7.5 + a = 8.077747211

Solving
7.5 + a = 8.077747211

Solving for variable 'a'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + a = 8.077747211 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + a = 8.077747211 + -7.5
a = 8.077747211 + -7.5

Combine like terms: 8.077747211 + -7.5 = 0.577747211
a = 0.577747211

Simplifying
a = 0.577747211


Subproblem 2
a + 7.5 = -8.077747211

Simplifying
a + 7.5 = -8.077747211

Reorder the terms:
7.5 + a = -8.077747211

Solving
7.5 + a = -8.077747211

Solving for variable 'a'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + a = -8.077747211 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + a = -8.077747211 + -7.5
a = -8.077747211 + -7.5

Combine like terms: -8.077747211 + -7.5 = -15.577747211
a = -15.577747211

Simplifying
a = -15.577747211


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.577747211, -15.577747211}

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