x^2-53x+144=0

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Solution for x^2-53x+144=0 equation: 


Simplifying
x2 + -53x + 144 = 0

Reorder the terms:
144 + -53x + x2 = 0

Solving
144 + -53x + 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 + -53x + -144 + x2 = 0 + -144

Reorder the terms:
144 + -144 + -53x + x2 = 0 + -144

Combine like terms: 144 + -144 = 0
0 + -53x + x2 = 0 + -144
-53x + x2 = 0 + -144

Combine like terms: 0 + -144 = -144
-53x + x2 = -144

The x term is -53x.  Take half its coefficient (-26.5).
Square it (702.25) and add it to both sides.

Add '702.25' to each side of the equation.
-53x + 702.25 + x2 = -144 + 702.25

Reorder the terms:
702.25 + -53x + x2 = -144 + 702.25

Combine like terms: -144 + 702.25 = 558.25
702.25 + -53x + x2 = 558.25

Factor a perfect square on the left side:
(x + -26.5)(x + -26.5) = 558.25

Calculate the square root of the right side: 23.627314701

Break this problem into two subproblems by setting 
(x + -26.5) equal to 23.627314701 and -23.627314701.


Subproblem 1
x + -26.5 = 23.627314701

Simplifying
x + -26.5 = 23.627314701

Reorder the terms:
-26.5 + x = 23.627314701

Solving
-26.5 + x = 23.627314701

Solving for variable 'x'.

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

Add '26.5' to each side of the equation.
-26.5 + 26.5 + x = 23.627314701 + 26.5

Combine like terms: -26.5 + 26.5 = 0.0
0.0 + x = 23.627314701 + 26.5
x = 23.627314701 + 26.5

Combine like terms: 23.627314701 + 26.5 = 50.127314701
x = 50.127314701

Simplifying
x = 50.127314701


Subproblem 2
x + -26.5 = -23.627314701

Simplifying
x + -26.5 = -23.627314701

Reorder the terms:
-26.5 + x = -23.627314701

Solving
-26.5 + x = -23.627314701

Solving for variable 'x'.

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

Add '26.5' to each side of the equation.
-26.5 + 26.5 + x = -23.627314701 + 26.5

Combine like terms: -26.5 + 26.5 = 0.0
0.0 + x = -23.627314701 + 26.5
x = -23.627314701 + 26.5

Combine like terms: -23.627314701 + 26.5 = 2.872685299
x = 2.872685299

Simplifying
x = 2.872685299


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {50.127314701, 2.872685299}

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