a^2+14a+49=45

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Solution for a^2+14a+49=45 equation: 


Simplifying
a2 + 14a + 49 = 45

Reorder the terms:
49 + 14a + a2 = 45

Solving
49 + 14a + a2 = 45

Solving for variable 'a'.

Reorder the terms:
49 + -45 + 14a + a2 = 45 + -45

Combine like terms: 49 + -45 = 4
4 + 14a + a2 = 45 + -45

Combine like terms: 45 + -45 = 0
4 + 14a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 14a + -4 + a2 = 0 + -4

Reorder the terms:
4 + -4 + 14a + a2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 14a + a2 = 0 + -4
14a + a2 = 0 + -4

Combine like terms: 0 + -4 = -4
14a + a2 = -4

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 = -4 + 49

Reorder the terms:
49 + 14a + a2 = -4 + 49

Combine like terms: -4 + 49 = 45
49 + 14a + a2 = 45

Factor a perfect square on the left side:
(a + 7)(a + 7) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(a + 7) equal to 6.708203933 and -6.708203933.


Subproblem 1
a + 7 = 6.708203933

Simplifying
a + 7 = 6.708203933

Reorder the terms:
7 + a = 6.708203933

Solving
7 + a = 6.708203933

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 = 6.708203933 + -7

Combine like terms: 7 + -7 = 0
0 + a = 6.708203933 + -7
a = 6.708203933 + -7

Combine like terms: 6.708203933 + -7 = -0.291796067
a = -0.291796067

Simplifying
a = -0.291796067


Subproblem 2
a + 7 = -6.708203933

Simplifying
a + 7 = -6.708203933

Reorder the terms:
7 + a = -6.708203933

Solving
7 + a = -6.708203933

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 = -6.708203933 + -7

Combine like terms: 7 + -7 = 0
0 + a = -6.708203933 + -7
a = -6.708203933 + -7

Combine like terms: -6.708203933 + -7 = -13.708203933
a = -13.708203933

Simplifying
a = -13.708203933


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.291796067, -13.708203933}

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