6x^2+24x-560=0

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Solution for 6x^2+24x-560=0 equation: 


Simplifying
6x2 + 24x + -560 = 0

Reorder the terms:
-560 + 24x + 6x2 = 0

Solving
-560 + 24x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-280 + 12x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-280 + 12x + 3x2)' equal to zero and attempt to solve:

Simplifying
-280 + 12x + 3x2 = 0

Solving
-280 + 12x + 3x2 = 0

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

Divide each side by '3'.
-93.33333333 + 4x + x2 = 0

Move the constant term to the right:

Add '93.33333333' to each side of the equation.
-93.33333333 + 4x + 93.33333333 + x2 = 0 + 93.33333333

Reorder the terms:
-93.33333333 + 93.33333333 + 4x + x2 = 0 + 93.33333333

Combine like terms: -93.33333333 + 93.33333333 = 0.00000000
0.00000000 + 4x + x2 = 0 + 93.33333333
4x + x2 = 0 + 93.33333333

Combine like terms: 0 + 93.33333333 = 93.33333333
4x + x2 = 93.33333333

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 93.33333333 + 4

Reorder the terms:
4 + 4x + x2 = 93.33333333 + 4

Combine like terms: 93.33333333 + 4 = 97.33333333
4 + 4x + x2 = 97.33333333

Factor a perfect square on the left side:
(x + 2)(x + 2) = 97.33333333

Calculate the square root of the right side: 9.865765724

Break this problem into two subproblems by setting 
(x + 2) equal to 9.865765724 and -9.865765724.


Subproblem 1
x + 2 = 9.865765724

Simplifying
x + 2 = 9.865765724

Reorder the terms:
2 + x = 9.865765724

Solving
2 + x = 9.865765724

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 9.865765724 + -2

Combine like terms: 2 + -2 = 0
0 + x = 9.865765724 + -2
x = 9.865765724 + -2

Combine like terms: 9.865765724 + -2 = 7.865765724
x = 7.865765724

Simplifying
x = 7.865765724


Subproblem 2
x + 2 = -9.865765724

Simplifying
x + 2 = -9.865765724

Reorder the terms:
2 + x = -9.865765724

Solving
2 + x = -9.865765724

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -9.865765724 + -2

Combine like terms: 2 + -2 = 0
0 + x = -9.865765724 + -2
x = -9.865765724 + -2

Combine like terms: -9.865765724 + -2 = -11.865765724
x = -11.865765724

Simplifying
x = -11.865765724


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.865765724, -11.865765724}
Solution
x = {7.865765724, -11.865765724}

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