a^2+15a+10=0

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Solution for a^2+15a+10=0 equation: 


Simplifying
a2 + 15a + 10 = 0

Reorder the terms:
10 + 15a + a2 = 0

Solving
10 + 15a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 15a + -10 + a2 = 0 + -10

Reorder the terms:
10 + -10 + 15a + a2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 15a + a2 = 0 + -10
15a + a2 = 0 + -10

Combine like terms: 0 + -10 = -10
15a + a2 = -10

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 = -10 + 56.25

Reorder the terms:
56.25 + 15a + a2 = -10 + 56.25

Combine like terms: -10 + 56.25 = 46.25
56.25 + 15a + a2 = 46.25

Factor a perfect square on the left side:
(a + 7.5)(a + 7.5) = 46.25

Calculate the square root of the right side: 6.800735254

Break this problem into two subproblems by setting 
(a + 7.5) equal to 6.800735254 and -6.800735254.


Subproblem 1
a + 7.5 = 6.800735254

Simplifying
a + 7.5 = 6.800735254

Reorder the terms:
7.5 + a = 6.800735254

Solving
7.5 + a = 6.800735254

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 = 6.800735254 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + a = 6.800735254 + -7.5
a = 6.800735254 + -7.5

Combine like terms: 6.800735254 + -7.5 = -0.699264746
a = -0.699264746

Simplifying
a = -0.699264746


Subproblem 2
a + 7.5 = -6.800735254

Simplifying
a + 7.5 = -6.800735254

Reorder the terms:
7.5 + a = -6.800735254

Solving
7.5 + a = -6.800735254

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 = -6.800735254 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + a = -6.800735254 + -7.5
a = -6.800735254 + -7.5

Combine like terms: -6.800735254 + -7.5 = -14.300735254
a = -14.300735254

Simplifying
a = -14.300735254


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.699264746, -14.300735254}

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