a^2+7a+8=0

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Solution for a^2+7a+8=0 equation: 


Simplifying
a2 + 7a + 8 = 0

Reorder the terms:
8 + 7a + a2 = 0

Solving
8 + 7a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 7a + -8 + a2 = 0 + -8

Reorder the terms:
8 + -8 + 7a + a2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 7a + a2 = 0 + -8
7a + a2 = 0 + -8

Combine like terms: 0 + -8 = -8
7a + a2 = -8

The a term is 7a.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7a + 12.25 + a2 = -8 + 12.25

Reorder the terms:
12.25 + 7a + a2 = -8 + 12.25

Combine like terms: -8 + 12.25 = 4.25
12.25 + 7a + a2 = 4.25

Factor a perfect square on the left side:
(a + 3.5)(a + 3.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(a + 3.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
a + 3.5 = 2.061552813

Simplifying
a + 3.5 = 2.061552813

Reorder the terms:
3.5 + a = 2.061552813

Solving
3.5 + a = 2.061552813

Solving for variable 'a'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + a = 2.061552813 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + a = 2.061552813 + -3.5
a = 2.061552813 + -3.5

Combine like terms: 2.061552813 + -3.5 = -1.438447187
a = -1.438447187

Simplifying
a = -1.438447187


Subproblem 2
a + 3.5 = -2.061552813

Simplifying
a + 3.5 = -2.061552813

Reorder the terms:
3.5 + a = -2.061552813

Solving
3.5 + a = -2.061552813

Solving for variable 'a'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + a = -2.061552813 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + a = -2.061552813 + -3.5
a = -2.061552813 + -3.5

Combine like terms: -2.061552813 + -3.5 = -5.561552813
a = -5.561552813

Simplifying
a = -5.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-1.438447187, -5.561552813}

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