2X^2-96X-576=0

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Solution for 2X^2-96X-576=0 equation: 


Simplifying
2X2 + -96X + -576 = 0

Reorder the terms:
-576 + -96X + 2X2 = 0

Solving
-576 + -96X + 2X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-288 + -48X + X2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-288 + -48X + X2)' equal to zero and attempt to solve:

Simplifying
-288 + -48X + X2 = 0

Solving
-288 + -48X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '288' to each side of the equation.
-288 + -48X + 288 + X2 = 0 + 288

Reorder the terms:
-288 + 288 + -48X + X2 = 0 + 288

Combine like terms: -288 + 288 = 0
0 + -48X + X2 = 0 + 288
-48X + X2 = 0 + 288

Combine like terms: 0 + 288 = 288
-48X + X2 = 288

The X term is -48X.  Take half its coefficient (-24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
-48X + 576 + X2 = 288 + 576

Reorder the terms:
576 + -48X + X2 = 288 + 576

Combine like terms: 288 + 576 = 864
576 + -48X + X2 = 864

Factor a perfect square on the left side:
(X + -24)(X + -24) = 864

Calculate the square root of the right side: 29.393876913

Break this problem into two subproblems by setting 
(X + -24) equal to 29.393876913 and -29.393876913.


Subproblem 1
X + -24 = 29.393876913

Simplifying
X + -24 = 29.393876913

Reorder the terms:
-24 + X = 29.393876913

Solving
-24 + X = 29.393876913

Solving for variable 'X'.

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

Add '24' to each side of the equation.
-24 + 24 + X = 29.393876913 + 24

Combine like terms: -24 + 24 = 0
0 + X = 29.393876913 + 24
X = 29.393876913 + 24

Combine like terms: 29.393876913 + 24 = 53.393876913
X = 53.393876913

Simplifying
X = 53.393876913


Subproblem 2
X + -24 = -29.393876913

Simplifying
X + -24 = -29.393876913

Reorder the terms:
-24 + X = -29.393876913

Solving
-24 + X = -29.393876913

Solving for variable 'X'.

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

Add '24' to each side of the equation.
-24 + 24 + X = -29.393876913 + 24

Combine like terms: -24 + 24 = 0
0 + X = -29.393876913 + 24
X = -29.393876913 + 24

Combine like terms: -29.393876913 + 24 = -5.393876913
X = -5.393876913

Simplifying
X = -5.393876913


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {53.393876913, -5.393876913}
Solution
X = {53.393876913, -5.393876913}

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