x^2-29x+144=0

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


Simplifying
x2 + -29x + 144 = 0

Reorder the terms:
144 + -29x + x2 = 0

Solving
144 + -29x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-144' to each side of the equation.
144 + -29x + -144 + x2 = 0 + -144

Reorder the terms:
144 + -144 + -29x + x2 = 0 + -144

Combine like terms: 144 + -144 = 0
0 + -29x + x2 = 0 + -144
-29x + x2 = 0 + -144

Combine like terms: 0 + -144 = -144
-29x + x2 = -144

The x term is -29x.  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.
-29x + 210.25 + x2 = -144 + 210.25

Reorder the terms:
210.25 + -29x + x2 = -144 + 210.25

Combine like terms: -144 + 210.25 = 66.25
210.25 + -29x + x2 = 66.25

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

Calculate the square root of the right side: 8.139410298

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


Subproblem 1
x + -14.5 = 8.139410298

Simplifying
x + -14.5 = 8.139410298

Reorder the terms:
-14.5 + x = 8.139410298

Solving
-14.5 + x = 8.139410298

Solving for variable 'x'.

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

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

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

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

Simplifying
x = 22.639410298


Subproblem 2
x + -14.5 = -8.139410298

Simplifying
x + -14.5 = -8.139410298

Reorder the terms:
-14.5 + x = -8.139410298

Solving
-14.5 + x = -8.139410298

Solving for variable 'x'.

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

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

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

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

Simplifying
x = 6.360589702


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

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