4x^2+28x-24=0

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Solution for 4x^2+28x-24=0 equation: 


Simplifying
4x2 + 28x + -24 = 0

Reorder the terms:
-24 + 28x + 4x2 = 0

Solving
-24 + 28x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + 7x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-6 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-6 + 7x + x2 = 0

Solving
-6 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 7x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 7x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 7x + x2 = 0 + 6
7x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
7x + x2 = 6

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 6 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 6 + 12.25

Combine like terms: 6 + 12.25 = 18.25
12.25 + 7x + x2 = 18.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
x + 3.5 = 4.272001873

Simplifying
x + 3.5 = 4.272001873

Reorder the terms:
3.5 + x = 4.272001873

Solving
3.5 + x = 4.272001873

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 4.272001873 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 4.272001873 + -3.5
x = 4.272001873 + -3.5

Combine like terms: 4.272001873 + -3.5 = 0.772001873
x = 0.772001873

Simplifying
x = 0.772001873


Subproblem 2
x + 3.5 = -4.272001873

Simplifying
x + 3.5 = -4.272001873

Reorder the terms:
3.5 + x = -4.272001873

Solving
3.5 + x = -4.272001873

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -4.272001873 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -4.272001873 + -3.5
x = -4.272001873 + -3.5

Combine like terms: -4.272001873 + -3.5 = -7.772001873
x = -7.772001873

Simplifying
x = -7.772001873


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.772001873, -7.772001873}
Solution
x = {0.772001873, -7.772001873}

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