6x^2+24x-76=0

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Solution for 6x^2+24x-76=0 equation: 


Simplifying
6x2 + 24x + -76 = 0

Reorder the terms:
-76 + 24x + 6x2 = 0

Solving
-76 + 24x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-38 + 12x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-38 + 12x + 3x2)' equal to zero and attempt to solve:

Simplifying
-38 + 12x + 3x2 = 0

Solving
-38 + 12x + 3x2 = 0

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

Divide each side by '3'.
-12.66666667 + 4x + x2 = 0

Move the constant term to the right:

Add '12.66666667' to each side of the equation.
-12.66666667 + 4x + 12.66666667 + x2 = 0 + 12.66666667

Reorder the terms:
-12.66666667 + 12.66666667 + 4x + x2 = 0 + 12.66666667

Combine like terms: -12.66666667 + 12.66666667 = 0.00000000
0.00000000 + 4x + x2 = 0 + 12.66666667
4x + x2 = 0 + 12.66666667

Combine like terms: 0 + 12.66666667 = 12.66666667
4x + x2 = 12.66666667

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 = 12.66666667 + 4

Reorder the terms:
4 + 4x + x2 = 12.66666667 + 4

Combine like terms: 12.66666667 + 4 = 16.66666667
4 + 4x + x2 = 16.66666667

Factor a perfect square on the left side:
(x + 2)(x + 2) = 16.66666667

Calculate the square root of the right side: 4.082482905

Break this problem into two subproblems by setting 
(x + 2) equal to 4.082482905 and -4.082482905.


Subproblem 1
x + 2 = 4.082482905

Simplifying
x + 2 = 4.082482905

Reorder the terms:
2 + x = 4.082482905

Solving
2 + x = 4.082482905

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 = 4.082482905 + -2

Combine like terms: 2 + -2 = 0
0 + x = 4.082482905 + -2
x = 4.082482905 + -2

Combine like terms: 4.082482905 + -2 = 2.082482905
x = 2.082482905

Simplifying
x = 2.082482905


Subproblem 2
x + 2 = -4.082482905

Simplifying
x + 2 = -4.082482905

Reorder the terms:
2 + x = -4.082482905

Solving
2 + x = -4.082482905

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 = -4.082482905 + -2

Combine like terms: 2 + -2 = 0
0 + x = -4.082482905 + -2
x = -4.082482905 + -2

Combine like terms: -4.082482905 + -2 = -6.082482905
x = -6.082482905

Simplifying
x = -6.082482905


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.082482905, -6.082482905}
Solution
x = {2.082482905, -6.082482905}

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