144x^2-432x-630=0

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Solution for 144x^2-432x-630=0 equation: 


Simplifying
144x2 + -432x + -630 = 0

Reorder the terms:
-630 + -432x + 144x2 = 0

Solving
-630 + -432x + 144x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '18'.
18(-35 + -24x + 8x2) = 0

Ignore the factor 18.

Subproblem 1
Set the factor '(-35 + -24x + 8x2)' equal to zero and attempt to solve:

Simplifying
-35 + -24x + 8x2 = 0

Solving
-35 + -24x + 8x2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-4.375 + -3x + x2 = 0

Move the constant term to the right:

Add '4.375' to each side of the equation.
-4.375 + -3x + 4.375 + x2 = 0 + 4.375

Reorder the terms:
-4.375 + 4.375 + -3x + x2 = 0 + 4.375

Combine like terms: -4.375 + 4.375 = 0.000
0.000 + -3x + x2 = 0 + 4.375
-3x + x2 = 0 + 4.375

Combine like terms: 0 + 4.375 = 4.375
-3x + x2 = 4.375

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 4.375 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 4.375 + 2.25

Combine like terms: 4.375 + 2.25 = 6.625
2.25 + -3x + x2 = 6.625

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 6.625

Calculate the square root of the right side: 2.573907535

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.573907535 and -2.573907535.


Subproblem 1
x + -1.5 = 2.573907535

Simplifying
x + -1.5 = 2.573907535

Reorder the terms:
-1.5 + x = 2.573907535

Solving
-1.5 + x = 2.573907535

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 2.573907535 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.573907535 + 1.5
x = 2.573907535 + 1.5

Combine like terms: 2.573907535 + 1.5 = 4.073907535
x = 4.073907535

Simplifying
x = 4.073907535


Subproblem 2
x + -1.5 = -2.573907535

Simplifying
x + -1.5 = -2.573907535

Reorder the terms:
-1.5 + x = -2.573907535

Solving
-1.5 + x = -2.573907535

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -2.573907535 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.573907535 + 1.5
x = -2.573907535 + 1.5

Combine like terms: -2.573907535 + 1.5 = -1.073907535
x = -1.073907535

Simplifying
x = -1.073907535


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.073907535, -1.073907535}
Solution
x = {4.073907535, -1.073907535}

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