a^2-29a+144=0

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Solution for a^2-29a+144=0 equation: 


Simplifying
a2 + -29a + 144 = 0

Reorder the terms:
144 + -29a + a2 = 0

Solving
144 + -29a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-144' to each side of the equation.
144 + -29a + -144 + a2 = 0 + -144

Reorder the terms:
144 + -144 + -29a + a2 = 0 + -144

Combine like terms: 144 + -144 = 0
0 + -29a + a2 = 0 + -144
-29a + a2 = 0 + -144

Combine like terms: 0 + -144 = -144
-29a + a2 = -144

The a term is -29a.  Take half its coefficient (-14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
-29a + 210.25 + a2 = -144 + 210.25

Reorder the terms:
210.25 + -29a + a2 = -144 + 210.25

Combine like terms: -144 + 210.25 = 66.25
210.25 + -29a + a2 = 66.25

Factor a perfect square on the left side:
(a + -14.5)(a + -14.5) = 66.25

Calculate the square root of the right side: 8.139410298

Break this problem into two subproblems by setting 
(a + -14.5) equal to 8.139410298 and -8.139410298.


Subproblem 1
a + -14.5 = 8.139410298

Simplifying
a + -14.5 = 8.139410298

Reorder the terms:
-14.5 + a = 8.139410298

Solving
-14.5 + a = 8.139410298

Solving for variable 'a'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + a = 8.139410298 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + a = 8.139410298 + 14.5
a = 8.139410298 + 14.5

Combine like terms: 8.139410298 + 14.5 = 22.639410298
a = 22.639410298

Simplifying
a = 22.639410298


Subproblem 2
a + -14.5 = -8.139410298

Simplifying
a + -14.5 = -8.139410298

Reorder the terms:
-14.5 + a = -8.139410298

Solving
-14.5 + a = -8.139410298

Solving for variable 'a'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + a = -8.139410298 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + a = -8.139410298 + 14.5
a = -8.139410298 + 14.5

Combine like terms: -8.139410298 + 14.5 = 6.360589702
a = 6.360589702

Simplifying
a = 6.360589702


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {22.639410298, 6.360589702}

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