4x^2+24x-8=0

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Solution for 4x^2+24x-8=0 equation: 


Simplifying
4x2 + 24x + -8 = 0

Reorder the terms:
-8 + 24x + 4x2 = 0

Solving
-8 + 24x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + 6x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-2 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + 6x + x2 = 0

Solving
-2 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 6x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 6x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 6x + x2 = 0 + 2
6x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
6x + x2 = 2

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 2 + 9

Reorder the terms:
9 + 6x + x2 = 2 + 9

Combine like terms: 2 + 9 = 11
9 + 6x + x2 = 11

Factor a perfect square on the left side:
(x + 3)(x + 3) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 3) equal to 3.31662479 and -3.31662479.


Subproblem 1
x + 3 = 3.31662479

Simplifying
x + 3 = 3.31662479

Reorder the terms:
3 + x = 3.31662479

Solving
3 + x = 3.31662479

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 3.31662479 + -3

Combine like terms: 3 + -3 = 0
0 + x = 3.31662479 + -3
x = 3.31662479 + -3

Combine like terms: 3.31662479 + -3 = 0.31662479
x = 0.31662479

Simplifying
x = 0.31662479


Subproblem 2
x + 3 = -3.31662479

Simplifying
x + 3 = -3.31662479

Reorder the terms:
3 + x = -3.31662479

Solving
3 + x = -3.31662479

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -3.31662479 + -3

Combine like terms: 3 + -3 = 0
0 + x = -3.31662479 + -3
x = -3.31662479 + -3

Combine like terms: -3.31662479 + -3 = -6.31662479
x = -6.31662479

Simplifying
x = -6.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.31662479, -6.31662479}
Solution
x = {0.31662479, -6.31662479}

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