a^2-14a-49=0

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Solution for a^2-14a-49=0 equation: 


Simplifying
a2 + -14a + -49 = 0

Reorder the terms:
-49 + -14a + a2 = 0

Solving
-49 + -14a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + -14a + 49 + a2 = 0 + 49

Reorder the terms:
-49 + 49 + -14a + a2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -14a + a2 = 0 + 49
-14a + a2 = 0 + 49

Combine like terms: 0 + 49 = 49
-14a + a2 = 49

The a term is -14a.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14a + 49 + a2 = 49 + 49

Reorder the terms:
49 + -14a + a2 = 49 + 49

Combine like terms: 49 + 49 = 98
49 + -14a + a2 = 98

Factor a perfect square on the left side:
(a + -7)(a + -7) = 98

Calculate the square root of the right side: 9.899494937

Break this problem into two subproblems by setting 
(a + -7) equal to 9.899494937 and -9.899494937.


Subproblem 1
a + -7 = 9.899494937

Simplifying
a + -7 = 9.899494937

Reorder the terms:
-7 + a = 9.899494937

Solving
-7 + a = 9.899494937

Solving for variable 'a'.

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

Add '7' to each side of the equation.
-7 + 7 + a = 9.899494937 + 7

Combine like terms: -7 + 7 = 0
0 + a = 9.899494937 + 7
a = 9.899494937 + 7

Combine like terms: 9.899494937 + 7 = 16.899494937
a = 16.899494937

Simplifying
a = 16.899494937


Subproblem 2
a + -7 = -9.899494937

Simplifying
a + -7 = -9.899494937

Reorder the terms:
-7 + a = -9.899494937

Solving
-7 + a = -9.899494937

Solving for variable 'a'.

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

Add '7' to each side of the equation.
-7 + 7 + a = -9.899494937 + 7

Combine like terms: -7 + 7 = 0
0 + a = -9.899494937 + 7
a = -9.899494937 + 7

Combine like terms: -9.899494937 + 7 = -2.899494937
a = -2.899494937

Simplifying
a = -2.899494937


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {16.899494937, -2.899494937}

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