48x^2-84x-352=0

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Solution for 48x^2-84x-352=0 equation: 


Simplifying
48x2 + -84x + -352 = 0

Reorder the terms:
-352 + -84x + 48x2 = 0

Solving
-352 + -84x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-88 + -21x + 12x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-88 + -21x + 12x2)' equal to zero and attempt to solve:

Simplifying
-88 + -21x + 12x2 = 0

Solving
-88 + -21x + 12x2 = 0

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

Divide each side by '12'.
-7.333333333 + -1.75x + x2 = 0

Move the constant term to the right:

Add '7.333333333' to each side of the equation.
-7.333333333 + -1.75x + 7.333333333 + x2 = 0 + 7.333333333

Reorder the terms:
-7.333333333 + 7.333333333 + -1.75x + x2 = 0 + 7.333333333

Combine like terms: -7.333333333 + 7.333333333 = 0.000000000
0.000000000 + -1.75x + x2 = 0 + 7.333333333
-1.75x + x2 = 0 + 7.333333333

Combine like terms: 0 + 7.333333333 = 7.333333333
-1.75x + x2 = 7.333333333

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 7.333333333 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 7.333333333 + 0.765625

Combine like terms: 7.333333333 + 0.765625 = 8.098958333
0.765625 + -1.75x + x2 = 8.098958333

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 8.098958333

Calculate the square root of the right side: 2.845866886

Break this problem into two subproblems by setting 
(x + -0.875) equal to 2.845866886 and -2.845866886.


Subproblem 1
x + -0.875 = 2.845866886

Simplifying
x + -0.875 = 2.845866886

Reorder the terms:
-0.875 + x = 2.845866886

Solving
-0.875 + x = 2.845866886

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = 2.845866886 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = 2.845866886 + 0.875
x = 2.845866886 + 0.875

Combine like terms: 2.845866886 + 0.875 = 3.720866886
x = 3.720866886

Simplifying
x = 3.720866886


Subproblem 2
x + -0.875 = -2.845866886

Simplifying
x + -0.875 = -2.845866886

Reorder the terms:
-0.875 + x = -2.845866886

Solving
-0.875 + x = -2.845866886

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = -2.845866886 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = -2.845866886 + 0.875
x = -2.845866886 + 0.875

Combine like terms: -2.845866886 + 0.875 = -1.970866886
x = -1.970866886

Simplifying
x = -1.970866886


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.720866886, -1.970866886}
Solution
x = {3.720866886, -1.970866886}

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