16x^2-24x-14=0

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Solution for 16x^2-24x-14=0 equation: 


Simplifying
16x2 + -24x + -14 = 0

Reorder the terms:
-14 + -24x + 16x2 = 0

Solving
-14 + -24x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -12x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -12x + 8x2)' equal to zero and attempt to solve:

Simplifying
-7 + -12x + 8x2 = 0

Solving
-7 + -12x + 8x2 = 0

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

Divide each side by '8'.
-0.875 + -1.5x + x2 = 0

Move the constant term to the right:

Add '0.875' to each side of the equation.
-0.875 + -1.5x + 0.875 + x2 = 0 + 0.875

Reorder the terms:
-0.875 + 0.875 + -1.5x + x2 = 0 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + -1.5x + x2 = 0 + 0.875
-1.5x + x2 = 0 + 0.875

Combine like terms: 0 + 0.875 = 0.875
-1.5x + x2 = 0.875

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 = 0.875 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 0.875 + 0.5625

Combine like terms: 0.875 + 0.5625 = 1.4375
0.5625 + -1.5x + x2 = 1.4375

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 1.4375

Calculate the square root of the right side: 1.198957881

Break this problem into two subproblems by setting 
(x + -0.75) equal to 1.198957881 and -1.198957881.


Subproblem 1
x + -0.75 = 1.198957881

Simplifying
x + -0.75 = 1.198957881

Reorder the terms:
-0.75 + x = 1.198957881

Solving
-0.75 + x = 1.198957881

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 = 1.198957881 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 1.198957881 + 0.75
x = 1.198957881 + 0.75

Combine like terms: 1.198957881 + 0.75 = 1.948957881
x = 1.948957881

Simplifying
x = 1.948957881


Subproblem 2
x + -0.75 = -1.198957881

Simplifying
x + -0.75 = -1.198957881

Reorder the terms:
-0.75 + x = -1.198957881

Solving
-0.75 + x = -1.198957881

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 = -1.198957881 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -1.198957881 + 0.75
x = -1.198957881 + 0.75

Combine like terms: -1.198957881 + 0.75 = -0.448957881
x = -0.448957881

Simplifying
x = -0.448957881


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.948957881, -0.448957881}
Solution
x = {1.948957881, -0.448957881}

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