2(x+3)(x+3)-5=98

Solution for 2(x+3)(x+3)-5=98 equation:

Simplifying
2(x + 3)(x + 3) + -5 = 98

Reorder the terms:
2(3 + x)(x + 3) + -5 = 98

Reorder the terms:
2(3 + x)(3 + x) + -5 = 98

Multiply (3 + x) * (3 + x)
2(3(3 + x) + x(3 + x)) + -5 = 98
2((3 * 3 + x * 3) + x(3 + x)) + -5 = 98
2((9 + 3x) + x(3 + x)) + -5 = 98
2(9 + 3x + (3 * x + x * x)) + -5 = 98
2(9 + 3x + (3x + x2)) + -5 = 98

Combine like terms: 3x + 3x = 6x
2(9 + 6x + x2) + -5 = 98
(9 * 2 + 6x * 2 + x2 * 2) + -5 = 98
(18 + 12x + 2x2) + -5 = 98

Reorder the terms:
18 + -5 + 12x + 2x2 = 98

Combine like terms: 18 + -5 = 13
13 + 12x + 2x2 = 98

Solving
13 + 12x + 2x2 = 98

Solving for variable 'x'.

Reorder the terms:
13 + -98 + 12x + 2x2 = 98 + -98

Combine like terms: 13 + -98 = -85
-85 + 12x + 2x2 = 98 + -98

Combine like terms: 98 + -98 = 0
-85 + 12x + 2x2 = 0

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

Divide each side by '2'.
-42.5 + 6x + x2 = 0

Move the constant term to the right:

Add '42.5' to each side of the equation.
-42.5 + 6x + 42.5 + x2 = 0 + 42.5

Reorder the terms:
-42.5 + 42.5 + 6x + x2 = 0 + 42.5

Combine like terms: -42.5 + 42.5 = 0.0
0.0 + 6x + x2 = 0 + 42.5
6x + x2 = 0 + 42.5

Combine like terms: 0 + 42.5 = 42.5
6x + x2 = 42.5

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 = 42.5 + 9

Reorder the terms:
9 + 6x + x2 = 42.5 + 9

Combine like terms: 42.5 + 9 = 51.5
9 + 6x + x2 = 51.5

Factor a perfect square on the left side:
(x + 3)(x + 3) = 51.5

Calculate the square root of the right side: 7.176350047

Break this problem into two subproblems by setting 
(x + 3) equal to 7.176350047 and -7.176350047.

Subproblem 1
x + 3 = 7.176350047

Simplifying
x + 3 = 7.176350047

Reorder the terms:
3 + x = 7.176350047

Solving
3 + x = 7.176350047

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 = 7.176350047 + -3

Combine like terms: 3 + -3 = 0
0 + x = 7.176350047 + -3
x = 7.176350047 + -3

Combine like terms: 7.176350047 + -3 = 4.176350047
x = 4.176350047

Simplifying
x = 4.176350047

Subproblem 2
x + 3 = -7.176350047

Simplifying
x + 3 = -7.176350047

Reorder the terms:
3 + x = -7.176350047

Solving
3 + x = -7.176350047

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 = -7.176350047 + -3

Combine like terms: 3 + -3 = 0
0 + x = -7.176350047 + -3
x = -7.176350047 + -3

Combine like terms: -7.176350047 + -3 = -10.176350047
x = -10.176350047

Simplifying
x = -10.176350047

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.176350047, -10.176350047}