16x^2-50x-30=0

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Solution for 16x^2-50x-30=0 equation: 


Simplifying
16x2 + -50x + -30 = 0

Reorder the terms:
-30 + -50x + 16x2 = 0

Solving
-30 + -50x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -25x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + -25x + 8x2)' equal to zero and attempt to solve:

Simplifying
-15 + -25x + 8x2 = 0

Solving
-15 + -25x + 8x2 = 0

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

Divide each side by '8'.
-1.875 + -3.125x + x2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + -3.125x + 1.875 + x2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + -3.125x + x2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + -3.125x + x2 = 0 + 1.875
-3.125x + x2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
-3.125x + x2 = 1.875

The x term is -3.125x.  Take half its coefficient (-1.5625).
Square it (2.44140625) and add it to both sides.

Add '2.44140625' to each side of the equation.
-3.125x + 2.44140625 + x2 = 1.875 + 2.44140625

Reorder the terms:
2.44140625 + -3.125x + x2 = 1.875 + 2.44140625

Combine like terms: 1.875 + 2.44140625 = 4.31640625
2.44140625 + -3.125x + x2 = 4.31640625

Factor a perfect square on the left side:
(x + -1.5625)(x + -1.5625) = 4.31640625

Calculate the square root of the right side: 2.077596267

Break this problem into two subproblems by setting 
(x + -1.5625) equal to 2.077596267 and -2.077596267.


Subproblem 1
x + -1.5625 = 2.077596267

Simplifying
x + -1.5625 = 2.077596267

Reorder the terms:
-1.5625 + x = 2.077596267

Solving
-1.5625 + x = 2.077596267

Solving for variable 'x'.

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

Add '1.5625' to each side of the equation.
-1.5625 + 1.5625 + x = 2.077596267 + 1.5625

Combine like terms: -1.5625 + 1.5625 = 0.0000
0.0000 + x = 2.077596267 + 1.5625
x = 2.077596267 + 1.5625

Combine like terms: 2.077596267 + 1.5625 = 3.640096267
x = 3.640096267

Simplifying
x = 3.640096267


Subproblem 2
x + -1.5625 = -2.077596267

Simplifying
x + -1.5625 = -2.077596267

Reorder the terms:
-1.5625 + x = -2.077596267

Solving
-1.5625 + x = -2.077596267

Solving for variable 'x'.

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

Add '1.5625' to each side of the equation.
-1.5625 + 1.5625 + x = -2.077596267 + 1.5625

Combine like terms: -1.5625 + 1.5625 = 0.0000
0.0000 + x = -2.077596267 + 1.5625
x = -2.077596267 + 1.5625

Combine like terms: -2.077596267 + 1.5625 = -0.515096267
x = -0.515096267

Simplifying
x = -0.515096267


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.640096267, -0.515096267}
Solution
x = {3.640096267, -0.515096267}

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