a^2-7a-7=0

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Solution for a^2-7a-7=0 equation: 


Simplifying
a2 + -7a + -7 = 0

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

Solving
-7 + -7a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 7 + 12.25

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

Combine like terms: 7 + 12.25 = 19.25
12.25 + -7a + a2 = 19.25

Factor a perfect square on the left side:
(a + -3.5)(a + -3.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(a + -3.5) equal to 4.387482194 and -4.387482194.


Subproblem 1
a + -3.5 = 4.387482194

Simplifying
a + -3.5 = 4.387482194

Reorder the terms:
-3.5 + a = 4.387482194

Solving
-3.5 + a = 4.387482194

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 = 4.387482194 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + a = 4.387482194 + 3.5
a = 4.387482194 + 3.5

Combine like terms: 4.387482194 + 3.5 = 7.887482194
a = 7.887482194

Simplifying
a = 7.887482194


Subproblem 2
a + -3.5 = -4.387482194

Simplifying
a + -3.5 = -4.387482194

Reorder the terms:
-3.5 + a = -4.387482194

Solving
-3.5 + a = -4.387482194

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 = -4.387482194 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + a = -4.387482194 + 3.5
a = -4.387482194 + 3.5

Combine like terms: -4.387482194 + 3.5 = -0.887482194
a = -0.887482194

Simplifying
a = -0.887482194


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {7.887482194, -0.887482194}

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