-16x^2+30x-4=0

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Solution for -16x^2+30x-4=0 equation: 


Simplifying
-16x2 + 30x + -4 = 0

Reorder the terms:
-4 + 30x + -16x2 = 0

Solving
-4 + 30x + -16x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 15x + -8x2)' equal to zero and attempt to solve:

Simplifying
-2 + 15x + -8x2 = 0

Solving
-2 + 15x + -8x2 = 0

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

Divide each side by '-8'.
0.25 + -1.875x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1.875x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -1.875x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1.875x + x2 = 0 + -0.25
-1.875x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-1.875x + x2 = -0.25

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 = -0.25 + 0.87890625

Reorder the terms:
0.87890625 + -1.875x + x2 = -0.25 + 0.87890625

Combine like terms: -0.25 + 0.87890625 = 0.62890625
0.87890625 + -1.875x + x2 = 0.62890625

Factor a perfect square on the left side:
(x + -0.9375)(x + -0.9375) = 0.62890625

Calculate the square root of the right side: 0.793036096

Break this problem into two subproblems by setting 
(x + -0.9375) equal to 0.793036096 and -0.793036096.


Subproblem 1
x + -0.9375 = 0.793036096

Simplifying
x + -0.9375 = 0.793036096

Reorder the terms:
-0.9375 + x = 0.793036096

Solving
-0.9375 + x = 0.793036096

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 = 0.793036096 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + x = 0.793036096 + 0.9375
x = 0.793036096 + 0.9375

Combine like terms: 0.793036096 + 0.9375 = 1.730536096
x = 1.730536096

Simplifying
x = 1.730536096


Subproblem 2
x + -0.9375 = -0.793036096

Simplifying
x + -0.9375 = -0.793036096

Reorder the terms:
-0.9375 + x = -0.793036096

Solving
-0.9375 + x = -0.793036096

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 = -0.793036096 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + x = -0.793036096 + 0.9375
x = -0.793036096 + 0.9375

Combine like terms: -0.793036096 + 0.9375 = 0.144463904
x = 0.144463904

Simplifying
x = 0.144463904


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.730536096, 0.144463904}
Solution
x = {1.730536096, 0.144463904}

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