16x^2+12x-164=0

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Solution for 16x^2+12x-164=0 equation:


Simplifying
16x2 + 12x + -164 = 0

Reorder the terms:
-164 + 12x + 16x2 = 0

Solving
-164 + 12x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-41 + 3x + 4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-41 + 3x + 4x2)' equal to zero and attempt to solve:

Simplifying
-41 + 3x + 4x2 = 0

Solving
-41 + 3x + 4x2 = 0

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

Divide each side by '4'.
-10.25 + 0.75x + x2 = 0

Move the constant term to the right:

Add '10.25' to each side of the equation.
-10.25 + 0.75x + 10.25 + x2 = 0 + 10.25

Reorder the terms:
-10.25 + 10.25 + 0.75x + x2 = 0 + 10.25

Combine like terms: -10.25 + 10.25 = 0.00
0.00 + 0.75x + x2 = 0 + 10.25
0.75x + x2 = 0 + 10.25

Combine like terms: 0 + 10.25 = 10.25
0.75x + x2 = 10.25

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 10.25 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 10.25 + 0.140625

Combine like terms: 10.25 + 0.140625 = 10.390625
0.140625 + 0.75x + x2 = 10.390625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 10.390625

Calculate the square root of the right side: 3.22344924

Break this problem into two subproblems by setting 
(x + 0.375) equal to 3.22344924 and -3.22344924.


Subproblem 1
x + 0.375 = 3.22344924

Simplifying
x + 0.375 = 3.22344924

Reorder the terms:
0.375 + x = 3.22344924

Solving
0.375 + x = 3.22344924

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 3.22344924 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 3.22344924 + -0.375
x = 3.22344924 + -0.375

Combine like terms: 3.22344924 + -0.375 = 2.84844924
x = 2.84844924

Simplifying
x = 2.84844924


Subproblem 2
x + 0.375 = -3.22344924

Simplifying
x + 0.375 = -3.22344924

Reorder the terms:
0.375 + x = -3.22344924

Solving
0.375 + x = -3.22344924

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -3.22344924 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -3.22344924 + -0.375
x = -3.22344924 + -0.375

Combine like terms: -3.22344924 + -0.375 = -3.59844924
x = -3.59844924

Simplifying
x = -3.59844924


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.84844924, -3.59844924}
Solution
x = {2.84844924, -3.59844924}

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