4x^2-24x-224=0

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Solution for 4x^2-24x-224=0 equation: 


Simplifying
4x2 + -24x + -224 = 0

Reorder the terms:
-224 + -24x + 4x2 = 0

Solving
-224 + -24x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-56 + -6x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-56 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-56 + -6x + x2 = 0

Solving
-56 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '56' to each side of the equation.
-56 + -6x + 56 + x2 = 0 + 56

Reorder the terms:
-56 + 56 + -6x + x2 = 0 + 56

Combine like terms: -56 + 56 = 0
0 + -6x + x2 = 0 + 56
-6x + x2 = 0 + 56

Combine like terms: 0 + 56 = 56
-6x + x2 = 56

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 = 56 + 9

Reorder the terms:
9 + -6x + x2 = 56 + 9

Combine like terms: 56 + 9 = 65
9 + -6x + x2 = 65

Factor a perfect square on the left side:
(x + -3)(x + -3) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(x + -3) equal to 8.062257748 and -8.062257748.


Subproblem 1
x + -3 = 8.062257748

Simplifying
x + -3 = 8.062257748

Reorder the terms:
-3 + x = 8.062257748

Solving
-3 + x = 8.062257748

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 = 8.062257748 + 3

Combine like terms: -3 + 3 = 0
0 + x = 8.062257748 + 3
x = 8.062257748 + 3

Combine like terms: 8.062257748 + 3 = 11.062257748
x = 11.062257748

Simplifying
x = 11.062257748


Subproblem 2
x + -3 = -8.062257748

Simplifying
x + -3 = -8.062257748

Reorder the terms:
-3 + x = -8.062257748

Solving
-3 + x = -8.062257748

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 = -8.062257748 + 3

Combine like terms: -3 + 3 = 0
0 + x = -8.062257748 + 3
x = -8.062257748 + 3

Combine like terms: -8.062257748 + 3 = -5.062257748
x = -5.062257748

Simplifying
x = -5.062257748


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.062257748, -5.062257748}
Solution
x = {11.062257748, -5.062257748}

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