300x^2-153x-1200=0

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Solution for 300x^2-153x-1200=0 equation: 


Simplifying
300x2 + -153x + -1200 = 0

Reorder the terms:
-1200 + -153x + 300x2 = 0

Solving
-1200 + -153x + 300x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-400 + -51x + 100x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-400 + -51x + 100x2)' equal to zero and attempt to solve:

Simplifying
-400 + -51x + 100x2 = 0

Solving
-400 + -51x + 100x2 = 0

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

Divide each side by '100'.
-4 + -0.51x + x2 = 0.00

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -0.51x + 4 + x2 = 0.00 + 4

Reorder the terms:
-4 + 4 + -0.51x + x2 = 0.00 + 4

Combine like terms: -4 + 4 = 0
0 + -0.51x + x2 = 0.00 + 4
-0.51x + x2 = 0.00 + 4

Combine like terms: 0.00 + 4 = 4
-0.51x + x2 = 4

The x term is -0.51x.  Take half its coefficient (-0.255).
Square it (0.065025) and add it to both sides.

Add '0.065025' to each side of the equation.
-0.51x + 0.065025 + x2 = 4 + 0.065025

Reorder the terms:
0.065025 + -0.51x + x2 = 4 + 0.065025

Combine like terms: 4 + 0.065025 = 4.065025
0.065025 + -0.51x + x2 = 4.065025

Factor a perfect square on the left side:
(x + -0.255)(x + -0.255) = 4.065025

Calculate the square root of the right side: 2.016190715

Break this problem into two subproblems by setting 
(x + -0.255) equal to 2.016190715 and -2.016190715.


Subproblem 1
x + -0.255 = 2.016190715

Simplifying
x + -0.255 = 2.016190715

Reorder the terms:
-0.255 + x = 2.016190715

Solving
-0.255 + x = 2.016190715

Solving for variable 'x'.

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

Add '0.255' to each side of the equation.
-0.255 + 0.255 + x = 2.016190715 + 0.255

Combine like terms: -0.255 + 0.255 = 0.000
0.000 + x = 2.016190715 + 0.255
x = 2.016190715 + 0.255

Combine like terms: 2.016190715 + 0.255 = 2.271190715
x = 2.271190715

Simplifying
x = 2.271190715


Subproblem 2
x + -0.255 = -2.016190715

Simplifying
x + -0.255 = -2.016190715

Reorder the terms:
-0.255 + x = -2.016190715

Solving
-0.255 + x = -2.016190715

Solving for variable 'x'.

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

Add '0.255' to each side of the equation.
-0.255 + 0.255 + x = -2.016190715 + 0.255

Combine like terms: -0.255 + 0.255 = 0.000
0.000 + x = -2.016190715 + 0.255
x = -2.016190715 + 0.255

Combine like terms: -2.016190715 + 0.255 = -1.761190715
x = -1.761190715

Simplifying
x = -1.761190715


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.271190715, -1.761190715}
Solution
x = {2.271190715, -1.761190715}

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