a^2-14a-52=0

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Solution for a^2-14a-52=0 equation: 


Simplifying
a2 + -14a + -52 = 0

Reorder the terms:
-52 + -14a + a2 = 0

Solving
-52 + -14a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '52' to each side of the equation.
-52 + -14a + 52 + a2 = 0 + 52

Reorder the terms:
-52 + 52 + -14a + a2 = 0 + 52

Combine like terms: -52 + 52 = 0
0 + -14a + a2 = 0 + 52
-14a + a2 = 0 + 52

Combine like terms: 0 + 52 = 52
-14a + a2 = 52

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 = 52 + 49

Reorder the terms:
49 + -14a + a2 = 52 + 49

Combine like terms: 52 + 49 = 101
49 + -14a + a2 = 101

Factor a perfect square on the left side:
(a + -7)(a + -7) = 101

Calculate the square root of the right side: 10.049875621

Break this problem into two subproblems by setting 
(a + -7) equal to 10.049875621 and -10.049875621.


Subproblem 1
a + -7 = 10.049875621

Simplifying
a + -7 = 10.049875621

Reorder the terms:
-7 + a = 10.049875621

Solving
-7 + a = 10.049875621

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 = 10.049875621 + 7

Combine like terms: -7 + 7 = 0
0 + a = 10.049875621 + 7
a = 10.049875621 + 7

Combine like terms: 10.049875621 + 7 = 17.049875621
a = 17.049875621

Simplifying
a = 17.049875621


Subproblem 2
a + -7 = -10.049875621

Simplifying
a + -7 = -10.049875621

Reorder the terms:
-7 + a = -10.049875621

Solving
-7 + a = -10.049875621

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 = -10.049875621 + 7

Combine like terms: -7 + 7 = 0
0 + a = -10.049875621 + 7
a = -10.049875621 + 7

Combine like terms: -10.049875621 + 7 = -3.049875621
a = -3.049875621

Simplifying
a = -3.049875621


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {17.049875621, -3.049875621}

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