2x^2+12x+16=196

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Solution for 2x^2+12x+16=196 equation: 


Simplifying
2x2 + 12x + 16 = 196

Reorder the terms:
16 + 12x + 2x2 = 196

Solving
16 + 12x + 2x2 = 196

Solving for variable 'x'.

Reorder the terms:
16 + -196 + 12x + 2x2 = 196 + -196

Combine like terms: 16 + -196 = -180
-180 + 12x + 2x2 = 196 + -196

Combine like terms: 196 + -196 = 0
-180 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + 6x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-90 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-90 + 6x + x2 = 0

Solving
-90 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 6x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 6x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 6x + x2 = 0 + 90
6x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
6x + x2 = 90

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 90 + 9

Reorder the terms:
9 + 6x + x2 = 90 + 9

Combine like terms: 90 + 9 = 99
9 + 6x + x2 = 99

Factor a perfect square on the left side:
(x + 3)(x + 3) = 99

Calculate the square root of the right side: 9.949874371

Break this problem into two subproblems by setting 
(x + 3) equal to 9.949874371 and -9.949874371.


Subproblem 1
x + 3 = 9.949874371

Simplifying
x + 3 = 9.949874371

Reorder the terms:
3 + x = 9.949874371

Solving
3 + x = 9.949874371

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 9.949874371 + -3

Combine like terms: 3 + -3 = 0
0 + x = 9.949874371 + -3
x = 9.949874371 + -3

Combine like terms: 9.949874371 + -3 = 6.949874371
x = 6.949874371

Simplifying
x = 6.949874371


Subproblem 2
x + 3 = -9.949874371

Simplifying
x + 3 = -9.949874371

Reorder the terms:
3 + x = -9.949874371

Solving
3 + x = -9.949874371

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -9.949874371 + -3

Combine like terms: 3 + -3 = 0
0 + x = -9.949874371 + -3
x = -9.949874371 + -3

Combine like terms: -9.949874371 + -3 = -12.949874371
x = -12.949874371

Simplifying
x = -12.949874371


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.949874371, -12.949874371}
Solution
x = {6.949874371, -12.949874371}

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