(16x^2-30x-10)=0

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Solution for (16x^2-30x-10)=0 equation: 


Simplifying
(16x2 + -30x + -10) = 0

Reorder the terms:
(-10 + -30x + 16x2) = 0

Remove parenthesis around (-10 + -30x + 16x2)
-10 + -30x + 16x2 = 0

Solving
-10 + -30x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -15x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -15x + 8x2)' equal to zero and attempt to solve:

Simplifying
-5 + -15x + 8x2 = 0

Solving
-5 + -15x + 8x2 = 0

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

Divide each side by '8'.
-0.625 + -1.875x + x2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + -1.875x + 0.625 + x2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + -1.875x + x2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + -1.875x + x2 = 0 + 0.625
-1.875x + x2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
-1.875x + x2 = 0.625

The x term is -1.875x.  Take half its coefficient (-0.9375).
Square it (0.87890625) and add it to both sides.

Add '0.87890625' to each side of the equation.
-1.875x + 0.87890625 + x2 = 0.625 + 0.87890625

Reorder the terms:
0.87890625 + -1.875x + x2 = 0.625 + 0.87890625

Combine like terms: 0.625 + 0.87890625 = 1.50390625
0.87890625 + -1.875x + x2 = 1.50390625

Factor a perfect square on the left side:
(x + -0.9375)(x + -0.9375) = 1.50390625

Calculate the square root of the right side: 1.226338554

Break this problem into two subproblems by setting 
(x + -0.9375) equal to 1.226338554 and -1.226338554.


Subproblem 1
x + -0.9375 = 1.226338554

Simplifying
x + -0.9375 = 1.226338554

Reorder the terms:
-0.9375 + x = 1.226338554

Solving
-0.9375 + x = 1.226338554

Solving for variable 'x'.

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

Add '0.9375' to each side of the equation.
-0.9375 + 0.9375 + x = 1.226338554 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + x = 1.226338554 + 0.9375
x = 1.226338554 + 0.9375

Combine like terms: 1.226338554 + 0.9375 = 2.163838554
x = 2.163838554

Simplifying
x = 2.163838554


Subproblem 2
x + -0.9375 = -1.226338554

Simplifying
x + -0.9375 = -1.226338554

Reorder the terms:
-0.9375 + x = -1.226338554

Solving
-0.9375 + x = -1.226338554

Solving for variable 'x'.

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

Add '0.9375' to each side of the equation.
-0.9375 + 0.9375 + x = -1.226338554 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + x = -1.226338554 + 0.9375
x = -1.226338554 + 0.9375

Combine like terms: -1.226338554 + 0.9375 = -0.288838554
x = -0.288838554

Simplifying
x = -0.288838554


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.163838554, -0.288838554}
Solution
x = {2.163838554, -0.288838554}

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