-16x^2+32x+5=7

Solution for -16x^2+32x+5=7 equation:

Simplifying
-16x2 + 32x + 5 = 7

Reorder the terms:
5 + 32x + -16x2 = 7

Solving
5 + 32x + -16x2 = 7

Solving for variable 'x'.

Reorder the terms:
5 + -7 + 32x + -16x2 = 7 + -7

Combine like terms: 5 + -7 = -2
-2 + 32x + -16x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-2 + 32x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 16x + -8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 16x + -8x2)' equal to zero and attempt to solve:

Simplifying
-1 + 16x + -8x2 = 0

Solving
-1 + 16x + -8x2 = 0

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

Divide each side by '-8'.
0.125 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -2x + -0.125 + x2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -2x + x2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -2x + x2 = 0 + -0.125
-2x + x2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-2x + x2 = -0.125

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.125 + 1

Reorder the terms:
1 + -2x + x2 = -0.125 + 1

Combine like terms: -0.125 + 1 = 0.875
1 + -2x + x2 = 0.875

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.875

Calculate the square root of the right side: 0.935414347

Break this problem into two subproblems by setting 
(x + -1) equal to 0.935414347 and -0.935414347.

Subproblem 1
x + -1 = 0.935414347

Simplifying
x + -1 = 0.935414347

Reorder the terms:
-1 + x = 0.935414347

Solving
-1 + x = 0.935414347

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 0.935414347 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.935414347 + 1
x = 0.935414347 + 1

Combine like terms: 0.935414347 + 1 = 1.935414347
x = 1.935414347

Simplifying
x = 1.935414347

Subproblem 2
x + -1 = -0.935414347

Simplifying
x + -1 = -0.935414347

Reorder the terms:
-1 + x = -0.935414347

Solving
-1 + x = -0.935414347

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -0.935414347 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.935414347 + 1
x = -0.935414347 + 1

Combine like terms: -0.935414347 + 1 = 0.064585653
x = 0.064585653

Simplifying
x = 0.064585653

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.935414347, 0.064585653}
Solution
x = {1.935414347, 0.064585653}