6x^2+26x-24=0

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Solution for 6x^2+26x-24=0 equation: 


Simplifying
6x2 + 26x + -24 = 0

Reorder the terms:
-24 + 26x + 6x2 = 0

Solving
-24 + 26x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 13x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-12 + 13x + 3x2)' equal to zero and attempt to solve:

Simplifying
-12 + 13x + 3x2 = 0

Solving
-12 + 13x + 3x2 = 0

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

Divide each side by '3'.
-4 + 4.333333333x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 4.333333333x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 4.333333333x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 4.333333333x + x2 = 0 + 4
4.333333333x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
4.333333333x + x2 = 4

The x term is 4.333333333x.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333x + 4.694444446 + x2 = 4 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333x + x2 = 4 + 4.694444446

Combine like terms: 4 + 4.694444446 = 8.694444446
4.694444446 + 4.333333333x + x2 = 8.694444446

Factor a perfect square on the left side:
(x + 2.166666667)(x + 2.166666667) = 8.694444446

Calculate the square root of the right side: 2.948634336

Break this problem into two subproblems by setting 
(x + 2.166666667) equal to 2.948634336 and -2.948634336.


Subproblem 1
x + 2.166666667 = 2.948634336

Simplifying
x + 2.166666667 = 2.948634336

Reorder the terms:
2.166666667 + x = 2.948634336

Solving
2.166666667 + x = 2.948634336

Solving for variable 'x'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x = 2.948634336 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x = 2.948634336 + -2.166666667
x = 2.948634336 + -2.166666667

Combine like terms: 2.948634336 + -2.166666667 = 0.781967669
x = 0.781967669

Simplifying
x = 0.781967669


Subproblem 2
x + 2.166666667 = -2.948634336

Simplifying
x + 2.166666667 = -2.948634336

Reorder the terms:
2.166666667 + x = -2.948634336

Solving
2.166666667 + x = -2.948634336

Solving for variable 'x'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x = -2.948634336 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x = -2.948634336 + -2.166666667
x = -2.948634336 + -2.166666667

Combine like terms: -2.948634336 + -2.166666667 = -5.115301003
x = -5.115301003

Simplifying
x = -5.115301003


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.781967669, -5.115301003}
Solution
x = {0.781967669, -5.115301003}

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