48x^2+24x-3=0

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Solution for 48x^2+24x-3=0 equation: 


Simplifying
48x2 + 24x + -3 = 0

Reorder the terms:
-3 + 24x + 48x2 = 0

Solving
-3 + 24x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 8x + 16x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1 + 8x + 16x2)' equal to zero and attempt to solve:

Simplifying
-1 + 8x + 16x2 = 0

Solving
-1 + 8x + 16x2 = 0

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

Divide each side by '16'.
-0.0625 + 0.5x + x2 = 0

Move the constant term to the right:

Add '0.0625' to each side of the equation.
-0.0625 + 0.5x + 0.0625 + x2 = 0 + 0.0625

Reorder the terms:
-0.0625 + 0.0625 + 0.5x + x2 = 0 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0000 + 0.5x + x2 = 0 + 0.0625
0.5x + x2 = 0 + 0.0625

Combine like terms: 0 + 0.0625 = 0.0625
0.5x + x2 = 0.0625

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 0.0625 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 0.0625 + 0.0625

Combine like terms: 0.0625 + 0.0625 = 0.125
0.0625 + 0.5x + x2 = 0.125

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 0.125

Calculate the square root of the right side: 0.353553391

Break this problem into two subproblems by setting 
(x + 0.25) equal to 0.353553391 and -0.353553391.


Subproblem 1
x + 0.25 = 0.353553391

Simplifying
x + 0.25 = 0.353553391

Reorder the terms:
0.25 + x = 0.353553391

Solving
0.25 + x = 0.353553391

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 0.353553391 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0.353553391 + -0.25
x = 0.353553391 + -0.25

Combine like terms: 0.353553391 + -0.25 = 0.103553391
x = 0.103553391

Simplifying
x = 0.103553391


Subproblem 2
x + 0.25 = -0.353553391

Simplifying
x + 0.25 = -0.353553391

Reorder the terms:
0.25 + x = -0.353553391

Solving
0.25 + x = -0.353553391

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -0.353553391 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -0.353553391 + -0.25
x = -0.353553391 + -0.25

Combine like terms: -0.353553391 + -0.25 = -0.603553391
x = -0.603553391

Simplifying
x = -0.603553391


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.103553391, -0.603553391}
Solution
x = {0.103553391, -0.603553391}

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