16x^2+16x+2=36

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Solution for 16x^2+16x+2=36 equation: 


Simplifying
16x2 + 16x + 2 = 36

Reorder the terms:
2 + 16x + 16x2 = 36

Solving
2 + 16x + 16x2 = 36

Solving for variable 'x'.

Reorder the terms:
2 + -36 + 16x + 16x2 = 36 + -36

Combine like terms: 2 + -36 = -34
-34 + 16x + 16x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-34 + 16x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + 8x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-17 + 8x + 8x2)' equal to zero and attempt to solve:

Simplifying
-17 + 8x + 8x2 = 0

Solving
-17 + 8x + 8x2 = 0

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

Divide each side by '8'.
-2.125 + x + x2 = 0

Move the constant term to the right:

Add '2.125' to each side of the equation.
-2.125 + x + 2.125 + x2 = 0 + 2.125

Reorder the terms:
-2.125 + 2.125 + x + x2 = 0 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + x + x2 = 0 + 2.125
x + x2 = 0 + 2.125

Combine like terms: 0 + 2.125 = 2.125
x + x2 = 2.125

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

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 2.125 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 2.125 + 0.25

Combine like terms: 2.125 + 0.25 = 2.375
1.25 + x2 = 2.375

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 2.375

Calculate the square root of the right side: 1.541103501

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.541103501 and -1.541103501.


Subproblem 1
x + 0.5 = 1.541103501

Simplifying
x + 0.5 = 1.541103501

Reorder the terms:
0.5 + x = 1.541103501

Solving
0.5 + x = 1.541103501

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.541103501 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.541103501 + -0.5
x = 1.541103501 + -0.5

Combine like terms: 1.541103501 + -0.5 = 1.041103501
x = 1.041103501

Simplifying
x = 1.041103501


Subproblem 2
x + 0.5 = -1.541103501

Simplifying
x + 0.5 = -1.541103501

Reorder the terms:
0.5 + x = -1.541103501

Solving
0.5 + x = -1.541103501

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.541103501 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.541103501 + -0.5
x = -1.541103501 + -0.5

Combine like terms: -1.541103501 + -0.5 = -2.041103501
x = -2.041103501

Simplifying
x = -2.041103501


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.041103501, -2.041103501}
Solution
x = {1.041103501, -2.041103501}

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