17-16x(6x+3)=-16

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Solution for 17-16x(6x+3)=-16 equation: 


Simplifying
17 + -16x(6x + 3) = -16

Reorder the terms:
17 + -16x(3 + 6x) = -16
17 + (3 * -16x + 6x * -16x) = -16
17 + (-48x + -96x2) = -16

Solving
17 + -48x + -96x2 = -16

Solving for variable 'x'.

Reorder the terms:
17 + 16 + -48x + -96x2 = -16 + 16

Combine like terms: 17 + 16 = 33
33 + -48x + -96x2 = -16 + 16

Combine like terms: -16 + 16 = 0
33 + -48x + -96x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(11 + -16x + -32x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(11 + -16x + -32x2)' equal to zero and attempt to solve:

Simplifying
11 + -16x + -32x2 = 0

Solving
11 + -16x + -32x2 = 0

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

Divide each side by '-32'.
-0.34375 + 0.5x + x2 = 0

Move the constant term to the right:

Add '0.34375' to each side of the equation.
-0.34375 + 0.5x + 0.34375 + x2 = 0 + 0.34375

Reorder the terms:
-0.34375 + 0.34375 + 0.5x + x2 = 0 + 0.34375

Combine like terms: -0.34375 + 0.34375 = 0.00000
0.00000 + 0.5x + x2 = 0 + 0.34375
0.5x + x2 = 0 + 0.34375

Combine like terms: 0 + 0.34375 = 0.34375
0.5x + x2 = 0.34375

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 0.34375 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 0.34375 + 0.0625

Combine like terms: 0.34375 + 0.0625 = 0.40625
0.0625 + 0.5x + x2 = 0.40625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 0.40625

Calculate the square root of the right side: 0.637377439

Break this problem into two subproblems by setting 
(x + 0.25) equal to 0.637377439 and -0.637377439.


Subproblem 1
x + 0.25 = 0.637377439

Simplifying
x + 0.25 = 0.637377439

Reorder the terms:
0.25 + x = 0.637377439

Solving
0.25 + x = 0.637377439

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 0.637377439 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0.637377439 + -0.25
x = 0.637377439 + -0.25

Combine like terms: 0.637377439 + -0.25 = 0.387377439
x = 0.387377439

Simplifying
x = 0.387377439


Subproblem 2
x + 0.25 = -0.637377439

Simplifying
x + 0.25 = -0.637377439

Reorder the terms:
0.25 + x = -0.637377439

Solving
0.25 + x = -0.637377439

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -0.637377439 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -0.637377439 + -0.25
x = -0.637377439 + -0.25

Combine like terms: -0.637377439 + -0.25 = -0.887377439
x = -0.887377439

Simplifying
x = -0.887377439


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.387377439, -0.887377439}
Solution
x = {0.387377439, -0.887377439}

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