24x^2+780x+1300=0

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Solution for 24x^2+780x+1300=0 equation: 


Simplifying
24x2 + 780x + 1300 = 0

Reorder the terms:
1300 + 780x + 24x2 = 0

Solving
1300 + 780x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(325 + 195x + 6x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(325 + 195x + 6x2)' equal to zero and attempt to solve:

Simplifying
325 + 195x + 6x2 = 0

Solving
325 + 195x + 6x2 = 0

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

Divide each side by '6'.
54.16666667 + 32.5x + x2 = 0

Move the constant term to the right:

Add '-54.16666667' to each side of the equation.
54.16666667 + 32.5x + -54.16666667 + x2 = 0 + -54.16666667

Reorder the terms:
54.16666667 + -54.16666667 + 32.5x + x2 = 0 + -54.16666667

Combine like terms: 54.16666667 + -54.16666667 = 0.00000000
0.00000000 + 32.5x + x2 = 0 + -54.16666667
32.5x + x2 = 0 + -54.16666667

Combine like terms: 0 + -54.16666667 = -54.16666667
32.5x + x2 = -54.16666667

The x term is 32.5x.  Take half its coefficient (16.25).
Square it (264.0625) and add it to both sides.

Add '264.0625' to each side of the equation.
32.5x + 264.0625 + x2 = -54.16666667 + 264.0625

Reorder the terms:
264.0625 + 32.5x + x2 = -54.16666667 + 264.0625

Combine like terms: -54.16666667 + 264.0625 = 209.89583333
264.0625 + 32.5x + x2 = 209.89583333

Factor a perfect square on the left side:
(x + 16.25)(x + 16.25) = 209.89583333

Calculate the square root of the right side: 14.487782209

Break this problem into two subproblems by setting 
(x + 16.25) equal to 14.487782209 and -14.487782209.


Subproblem 1
x + 16.25 = 14.487782209

Simplifying
x + 16.25 = 14.487782209

Reorder the terms:
16.25 + x = 14.487782209

Solving
16.25 + x = 14.487782209

Solving for variable 'x'.

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

Add '-16.25' to each side of the equation.
16.25 + -16.25 + x = 14.487782209 + -16.25

Combine like terms: 16.25 + -16.25 = 0.00
0.00 + x = 14.487782209 + -16.25
x = 14.487782209 + -16.25

Combine like terms: 14.487782209 + -16.25 = -1.762217791
x = -1.762217791

Simplifying
x = -1.762217791


Subproblem 2
x + 16.25 = -14.487782209

Simplifying
x + 16.25 = -14.487782209

Reorder the terms:
16.25 + x = -14.487782209

Solving
16.25 + x = -14.487782209

Solving for variable 'x'.

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

Add '-16.25' to each side of the equation.
16.25 + -16.25 + x = -14.487782209 + -16.25

Combine like terms: 16.25 + -16.25 = 0.00
0.00 + x = -14.487782209 + -16.25
x = -14.487782209 + -16.25

Combine like terms: -14.487782209 + -16.25 = -30.737782209
x = -30.737782209

Simplifying
x = -30.737782209


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.762217791, -30.737782209}
Solution
x = {-1.762217791, -30.737782209}

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