x^2-53x=144

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


Simplifying
x2 + -53x = 144

Reorder the terms:
-53x + x2 = 144

Solving
-53x + x2 = 144

Solving for variable 'x'.

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

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

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 = 846.25
702.25 + -53x + x2 = 846.25

Factor a perfect square on the left side:
(x + -26.5)(x + -26.5) = 846.25

Calculate the square root of the right side: 29.090376416

Break this problem into two subproblems by setting 
(x + -26.5) equal to 29.090376416 and -29.090376416.


Subproblem 1
x + -26.5 = 29.090376416

Simplifying
x + -26.5 = 29.090376416

Reorder the terms:
-26.5 + x = 29.090376416

Solving
-26.5 + x = 29.090376416

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 = 29.090376416 + 26.5

Combine like terms: -26.5 + 26.5 = 0.0
0.0 + x = 29.090376416 + 26.5
x = 29.090376416 + 26.5

Combine like terms: 29.090376416 + 26.5 = 55.590376416
x = 55.590376416

Simplifying
x = 55.590376416


Subproblem 2
x + -26.5 = -29.090376416

Simplifying
x + -26.5 = -29.090376416

Reorder the terms:
-26.5 + x = -29.090376416

Solving
-26.5 + x = -29.090376416

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 = -29.090376416 + 26.5

Combine like terms: -26.5 + 26.5 = 0.0
0.0 + x = -29.090376416 + 26.5
x = -29.090376416 + 26.5

Combine like terms: -29.090376416 + 26.5 = -2.590376416
x = -2.590376416

Simplifying
x = -2.590376416


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {55.590376416, -2.590376416}

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