16x^2-24x-5=0

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Solution for 16x^2-24x-5=0 equation: 


Simplifying
16x2 + -24x + -5 = 0

Reorder the terms:
-5 + -24x + 16x2 = 0

Solving
-5 + -24x + 16x2 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
-0.3125 + -1.5x + x2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + -1.5x + 0.3125 + x2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + -1.5x + x2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + -1.5x + x2 = 0 + 0.3125
-1.5x + x2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
-1.5x + x2 = 0.3125

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 = 0.3125 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 0.3125 + 0.5625

Combine like terms: 0.3125 + 0.5625 = 0.875
0.5625 + -1.5x + x2 = 0.875

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 0.875

Calculate the square root of the right side: 0.935414347

Break this problem into two subproblems by setting 
(x + -0.75) equal to 0.935414347 and -0.935414347.


Subproblem 1
x + -0.75 = 0.935414347

Simplifying
x + -0.75 = 0.935414347

Reorder the terms:
-0.75 + x = 0.935414347

Solving
-0.75 + x = 0.935414347

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 = 0.935414347 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 0.935414347 + 0.75
x = 0.935414347 + 0.75

Combine like terms: 0.935414347 + 0.75 = 1.685414347
x = 1.685414347

Simplifying
x = 1.685414347


Subproblem 2
x + -0.75 = -0.935414347

Simplifying
x + -0.75 = -0.935414347

Reorder the terms:
-0.75 + x = -0.935414347

Solving
-0.75 + x = -0.935414347

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 = -0.935414347 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -0.935414347 + 0.75
x = -0.935414347 + 0.75

Combine like terms: -0.935414347 + 0.75 = -0.185414347
x = -0.185414347

Simplifying
x = -0.185414347


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.685414347, -0.185414347}

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