a^2-45+14a=0

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Solution for a^2-45+14a=0 equation: 


Simplifying
a2 + -45 + 14a = 0

Reorder the terms:
-45 + 14a + a2 = 0

Solving
-45 + 14a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 14a + 45 + a2 = 0 + 45

Reorder the terms:
-45 + 45 + 14a + a2 = 0 + 45

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

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

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 = 45 + 49

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

Combine like terms: 45 + 49 = 94
49 + 14a + a2 = 94

Factor a perfect square on the left side:
(a + 7)(a + 7) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(a + 7) equal to 9.695359715 and -9.695359715.


Subproblem 1
a + 7 = 9.695359715

Simplifying
a + 7 = 9.695359715

Reorder the terms:
7 + a = 9.695359715

Solving
7 + a = 9.695359715

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 = 9.695359715 + -7

Combine like terms: 7 + -7 = 0
0 + a = 9.695359715 + -7
a = 9.695359715 + -7

Combine like terms: 9.695359715 + -7 = 2.695359715
a = 2.695359715

Simplifying
a = 2.695359715


Subproblem 2
a + 7 = -9.695359715

Simplifying
a + 7 = -9.695359715

Reorder the terms:
7 + a = -9.695359715

Solving
7 + a = -9.695359715

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 = -9.695359715 + -7

Combine like terms: 7 + -7 = 0
0 + a = -9.695359715 + -7
a = -9.695359715 + -7

Combine like terms: -9.695359715 + -7 = -16.695359715
a = -16.695359715

Simplifying
a = -16.695359715


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.695359715, -16.695359715}

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