16x^2-24x-4=0

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Solution for 16x^2-24x-4=0 equation: 


Simplifying
16x2 + -24x + -4 = 0

Reorder the terms:
-4 + -24x + 16x2 = 0

Solving
-4 + -24x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -6x + 4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1 + -6x + 4x2)' equal to zero and attempt to solve:

Simplifying
-1 + -6x + 4x2 = 0

Solving
-1 + -6x + 4x2 = 0

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

Divide each side by '4'.
-0.25 + -1.5x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -1.5x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -1.5x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -1.5x + x2 = 0 + 0.25
-1.5x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-1.5x + x2 = 0.25

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 0.25 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 0.25 + 0.5625

Combine like terms: 0.25 + 0.5625 = 0.8125
0.5625 + -1.5x + x2 = 0.8125

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 0.8125

Calculate the square root of the right side: 0.901387819

Break this problem into two subproblems by setting 
(x + -0.75) equal to 0.901387819 and -0.901387819.


Subproblem 1
x + -0.75 = 0.901387819

Simplifying
x + -0.75 = 0.901387819

Reorder the terms:
-0.75 + x = 0.901387819

Solving
-0.75 + x = 0.901387819

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 0.901387819 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 0.901387819 + 0.75
x = 0.901387819 + 0.75

Combine like terms: 0.901387819 + 0.75 = 1.651387819
x = 1.651387819

Simplifying
x = 1.651387819


Subproblem 2
x + -0.75 = -0.901387819

Simplifying
x + -0.75 = -0.901387819

Reorder the terms:
-0.75 + x = -0.901387819

Solving
-0.75 + x = -0.901387819

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -0.901387819 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -0.901387819 + 0.75
x = -0.901387819 + 0.75

Combine like terms: -0.901387819 + 0.75 = -0.151387819
x = -0.151387819

Simplifying
x = -0.151387819


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.651387819, -0.151387819}
Solution
x = {1.651387819, -0.151387819}

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