(7x+1)(7x-1)-49(x+1)=4-98x

Solution for (7x+1)(7x-1)-49(x+1)=4-98x equation:

Simplifying
(7x + 1)(7x + -1) + -49(x + 1) = 4 + -98x

Reorder the terms:
(1 + 7x)(7x + -1) + -49(x + 1) = 4 + -98x

Reorder the terms:
(1 + 7x)(-1 + 7x) + -49(x + 1) = 4 + -98x

Multiply (1 + 7x) * (-1 + 7x)
(1(-1 + 7x) + 7x * (-1 + 7x)) + -49(x + 1) = 4 + -98x
((-1 * 1 + 7x * 1) + 7x * (-1 + 7x)) + -49(x + 1) = 4 + -98x
((-1 + 7x) + 7x * (-1 + 7x)) + -49(x + 1) = 4 + -98x
(-1 + 7x + (-1 * 7x + 7x * 7x)) + -49(x + 1) = 4 + -98x
(-1 + 7x + (-7x + 49x2)) + -49(x + 1) = 4 + -98x

Combine like terms: 7x + -7x = 0
(-1 + 0 + 49x2) + -49(x + 1) = 4 + -98x
(-1 + 49x2) + -49(x + 1) = 4 + -98x

Reorder the terms:
-1 + 49x2 + -49(1 + x) = 4 + -98x
-1 + 49x2 + (1 * -49 + x * -49) = 4 + -98x
-1 + 49x2 + (-49 + -49x) = 4 + -98x

Reorder the terms:
-1 + -49 + -49x + 49x2 = 4 + -98x

Combine like terms: -1 + -49 = -50
-50 + -49x + 49x2 = 4 + -98x

Solving
-50 + -49x + 49x2 = 4 + -98x

Solving for variable 'x'.

Reorder the terms:
-50 + -4 + -49x + 98x + 49x2 = 4 + -98x + -4 + 98x

Combine like terms: -50 + -4 = -54
-54 + -49x + 98x + 49x2 = 4 + -98x + -4 + 98x

Combine like terms: -49x + 98x = 49x
-54 + 49x + 49x2 = 4 + -98x + -4 + 98x

Reorder the terms:
-54 + 49x + 49x2 = 4 + -4 + -98x + 98x

Combine like terms: 4 + -4 = 0
-54 + 49x + 49x2 = 0 + -98x + 98x
-54 + 49x + 49x2 = -98x + 98x

Combine like terms: -98x + 98x = 0
-54 + 49x + 49x2 = 0

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

Divide each side by '49'.
-1.102040816 + x + x2 = 0

Move the constant term to the right:

Add '1.102040816' to each side of the equation.
-1.102040816 + x + 1.102040816 + x2 = 0 + 1.102040816

Reorder the terms:
-1.102040816 + 1.102040816 + x + x2 = 0 + 1.102040816

Combine like terms: -1.102040816 + 1.102040816 = 0.000000000
0.000000000 + x + x2 = 0 + 1.102040816
x + x2 = 0 + 1.102040816

Combine like terms: 0 + 1.102040816 = 1.102040816
x + x2 = 1.102040816

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 = 1.102040816 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 1.102040816 + 0.25

Combine like terms: 1.102040816 + 0.25 = 1.352040816
1.25 + x2 = 1.352040816

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.352040816

Calculate the square root of the right side: 1.1627729

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.1627729 and -1.1627729.

Subproblem 1
x + 0.5 = 1.1627729

Simplifying
x + 0.5 = 1.1627729

Reorder the terms:
0.5 + x = 1.1627729

Solving
0.5 + x = 1.1627729

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 = 1.1627729 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.1627729 + -0.5
x = 1.1627729 + -0.5

Combine like terms: 1.1627729 + -0.5 = 0.6627729
x = 0.6627729

Simplifying
x = 0.6627729

Subproblem 2
x + 0.5 = -1.1627729

Simplifying
x + 0.5 = -1.1627729

Reorder the terms:
0.5 + x = -1.1627729

Solving
0.5 + x = -1.1627729

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 = -1.1627729 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.1627729 + -0.5
x = -1.1627729 + -0.5

Combine like terms: -1.1627729 + -0.5 = -1.6627729
x = -1.6627729

Simplifying
x = -1.6627729

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6627729, -1.6627729}