-16x^2+47x+5=0

Solution for -16x^2+47x+5=0 equation:

Simplifying
-16x2 + 47x + 5 = 0

Reorder the terms:
5 + 47x + -16x2 = 0

Solving
5 + 47x + -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 + -2.9375x + x2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + -2.9375x + 0.3125 + x2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + -2.9375x + x2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + -2.9375x + x2 = 0 + 0.3125
-2.9375x + x2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
-2.9375x + x2 = 0.3125

The x term is -2.9375x.  Take half its coefficient (-1.46875).
Square it (2.157226563) and add it to both sides.

Add '2.157226563' to each side of the equation.
-2.9375x + 2.157226563 + x2 = 0.3125 + 2.157226563

Reorder the terms:
2.157226563 + -2.9375x + x2 = 0.3125 + 2.157226563

Combine like terms: 0.3125 + 2.157226563 = 2.469726563
2.157226563 + -2.9375x + x2 = 2.469726563

Factor a perfect square on the left side:
(x + -1.46875)(x + -1.46875) = 2.469726563

Calculate the square root of the right side: 1.57153637

Break this problem into two subproblems by setting 
(x + -1.46875) equal to 1.57153637 and -1.57153637.

Subproblem 1
x + -1.46875 = 1.57153637

Simplifying
x + -1.46875 = 1.57153637

Reorder the terms:
-1.46875 + x = 1.57153637

Solving
-1.46875 + x = 1.57153637

Solving for variable 'x'.

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

Add '1.46875' to each side of the equation.
-1.46875 + 1.46875 + x = 1.57153637 + 1.46875

Combine like terms: -1.46875 + 1.46875 = 0.00000
0.00000 + x = 1.57153637 + 1.46875
x = 1.57153637 + 1.46875

Combine like terms: 1.57153637 + 1.46875 = 3.04028637
x = 3.04028637

Simplifying
x = 3.04028637

Subproblem 2
x + -1.46875 = -1.57153637

Simplifying
x + -1.46875 = -1.57153637

Reorder the terms:
-1.46875 + x = -1.57153637

Solving
-1.46875 + x = -1.57153637

Solving for variable 'x'.

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

Add '1.46875' to each side of the equation.
-1.46875 + 1.46875 + x = -1.57153637 + 1.46875

Combine like terms: -1.46875 + 1.46875 = 0.00000
0.00000 + x = -1.57153637 + 1.46875
x = -1.57153637 + 1.46875

Combine like terms: -1.57153637 + 1.46875 = -0.10278637
x = -0.10278637

Simplifying
x = -0.10278637

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.04028637, -0.10278637}