30x^2-45x-600=0

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Solution for 30x^2-45x-600=0 equation: 


Simplifying
30x2 + -45x + -600 = 0

Reorder the terms:
-600 + -45x + 30x2 = 0

Solving
-600 + -45x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '15'.
15(-40 + -3x + 2x2) = 0

Ignore the factor 15.

Subproblem 1
Set the factor '(-40 + -3x + 2x2)' equal to zero and attempt to solve:

Simplifying
-40 + -3x + 2x2 = 0

Solving
-40 + -3x + 2x2 = 0

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

Divide each side by '2'.
-20 + -1.5x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -1.5x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -1.5x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1.5x + x2 = 0 + 20
-1.5x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-1.5x + x2 = 20

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 20 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 20 + 0.5625

Combine like terms: 20 + 0.5625 = 20.5625
0.5625 + -1.5x + x2 = 20.5625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 20.5625

Calculate the square root of the right side: 4.534589287

Break this problem into two subproblems by setting 
(x + -0.75) equal to 4.534589287 and -4.534589287.


Subproblem 1
x + -0.75 = 4.534589287

Simplifying
x + -0.75 = 4.534589287

Reorder the terms:
-0.75 + x = 4.534589287

Solving
-0.75 + x = 4.534589287

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 4.534589287 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 4.534589287 + 0.75
x = 4.534589287 + 0.75

Combine like terms: 4.534589287 + 0.75 = 5.284589287
x = 5.284589287

Simplifying
x = 5.284589287


Subproblem 2
x + -0.75 = -4.534589287

Simplifying
x + -0.75 = -4.534589287

Reorder the terms:
-0.75 + x = -4.534589287

Solving
-0.75 + x = -4.534589287

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -4.534589287 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -4.534589287 + 0.75
x = -4.534589287 + 0.75

Combine like terms: -4.534589287 + 0.75 = -3.784589287
x = -3.784589287

Simplifying
x = -3.784589287


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.284589287, -3.784589287}
Solution
x = {5.284589287, -3.784589287}

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