32x^2-54x-5=

Solution for 32x^2-54x-5= equation:

Simplifying
32x2 + -54x + -5 = 0

Reorder the terms:
-5 + -54x + 32x2 = 0

Solving
-5 + -54x + 32x2 = 0

Solving for variable 'x'.

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

Divide each side by '32'.
-0.15625 + -1.6875x + x2 = 0

Move the constant term to the right:

Add '0.15625' to each side of the equation.
-0.15625 + -1.6875x + 0.15625 + x2 = 0 + 0.15625

Reorder the terms:
-0.15625 + 0.15625 + -1.6875x + x2 = 0 + 0.15625

Combine like terms: -0.15625 + 0.15625 = 0.00000
0.00000 + -1.6875x + x2 = 0 + 0.15625
-1.6875x + x2 = 0 + 0.15625

Combine like terms: 0 + 0.15625 = 0.15625
-1.6875x + x2 = 0.15625

The x term is -1.6875x.  Take half its coefficient (-0.84375).
Square it (0.7119140625) and add it to both sides.

Add '0.7119140625' to each side of the equation.
-1.6875x + 0.7119140625 + x2 = 0.15625 + 0.7119140625

Reorder the terms:
0.7119140625 + -1.6875x + x2 = 0.15625 + 0.7119140625

Combine like terms: 0.15625 + 0.7119140625 = 0.8681640625
0.7119140625 + -1.6875x + x2 = 0.8681640625

Factor a perfect square on the left side:
(x + -0.84375)(x + -0.84375) = 0.8681640625

Calculate the square root of the right side: 0.93175322

Break this problem into two subproblems by setting 
(x + -0.84375) equal to 0.93175322 and -0.93175322.

Subproblem 1
x + -0.84375 = 0.93175322

Simplifying
x + -0.84375 = 0.93175322

Reorder the terms:
-0.84375 + x = 0.93175322

Solving
-0.84375 + x = 0.93175322

Solving for variable 'x'.

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

Add '0.84375' to each side of the equation.
-0.84375 + 0.84375 + x = 0.93175322 + 0.84375

Combine like terms: -0.84375 + 0.84375 = 0.00000
0.00000 + x = 0.93175322 + 0.84375
x = 0.93175322 + 0.84375

Combine like terms: 0.93175322 + 0.84375 = 1.77550322
x = 1.77550322

Simplifying
x = 1.77550322

Subproblem 2
x + -0.84375 = -0.93175322

Simplifying
x + -0.84375 = -0.93175322

Reorder the terms:
-0.84375 + x = -0.93175322

Solving
-0.84375 + x = -0.93175322

Solving for variable 'x'.

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

Add '0.84375' to each side of the equation.
-0.84375 + 0.84375 + x = -0.93175322 + 0.84375

Combine like terms: -0.84375 + 0.84375 = 0.00000
0.00000 + x = -0.93175322 + 0.84375
x = -0.93175322 + 0.84375

Combine like terms: -0.93175322 + 0.84375 = -0.08800322
x = -0.08800322

Simplifying
x = -0.08800322

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.77550322, -0.08800322}