(49x^2-1)+3x(7x-1)=7x+1

Solution for (49x^2-1)+3x(7x-1)=7x+1 equation:

Simplifying
(49x2 + -1) + 3x(7x + -1) = 7x + 1

Reorder the terms:
(-1 + 49x2) + 3x(7x + -1) = 7x + 1

Remove parenthesis around (-1 + 49x2)
-1 + 49x2 + 3x(7x + -1) = 7x + 1

Reorder the terms:
-1 + 49x2 + 3x(-1 + 7x) = 7x + 1
-1 + 49x2 + (-1 * 3x + 7x * 3x) = 7x + 1
-1 + 49x2 + (-3x + 21x2) = 7x + 1

Reorder the terms:
-1 + -3x + 49x2 + 21x2 = 7x + 1

Combine like terms: 49x2 + 21x2 = 70x2
-1 + -3x + 70x2 = 7x + 1

Reorder the terms:
-1 + -3x + 70x2 = 1 + 7x

Solving
-1 + -3x + 70x2 = 1 + 7x

Solving for variable 'x'.

Reorder the terms:
-1 + -1 + -3x + -7x + 70x2 = 1 + 7x + -1 + -7x

Combine like terms: -1 + -1 = -2
-2 + -3x + -7x + 70x2 = 1 + 7x + -1 + -7x

Combine like terms: -3x + -7x = -10x
-2 + -10x + 70x2 = 1 + 7x + -1 + -7x

Reorder the terms:
-2 + -10x + 70x2 = 1 + -1 + 7x + -7x

Combine like terms: 1 + -1 = 0
-2 + -10x + 70x2 = 0 + 7x + -7x
-2 + -10x + 70x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-2 + -10x + 70x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -5x + 35x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -5x + 35x2)' equal to zero and attempt to solve:

Simplifying
-1 + -5x + 35x2 = 0

Solving
-1 + -5x + 35x2 = 0

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

Divide each side by '35'.
-0.02857142857 + -0.1428571429x + x2 = 0

Move the constant term to the right:

Add '0.02857142857' to each side of the equation.
-0.02857142857 + -0.1428571429x + 0.02857142857 + x2 = 0 + 0.02857142857

Reorder the terms:
-0.02857142857 + 0.02857142857 + -0.1428571429x + x2 = 0 + 0.02857142857

Combine like terms: -0.02857142857 + 0.02857142857 = 0.00000000000
0.00000000000 + -0.1428571429x + x2 = 0 + 0.02857142857
-0.1428571429x + x2 = 0 + 0.02857142857

Combine like terms: 0 + 0.02857142857 = 0.02857142857
-0.1428571429x + x2 = 0.02857142857

The x term is -0.1428571429x.  Take half its coefficient (-0.07142857145).
Square it (0.005102040819) and add it to both sides.

Add '0.005102040819' to each side of the equation.
-0.1428571429x + 0.005102040819 + x2 = 0.02857142857 + 0.005102040819

Reorder the terms:
0.005102040819 + -0.1428571429x + x2 = 0.02857142857 + 0.005102040819

Combine like terms: 0.02857142857 + 0.005102040819 = 0.033673469389
0.005102040819 + -0.1428571429x + x2 = 0.033673469389

Factor a perfect square on the left side:
(x + -0.07142857145)(x + -0.07142857145) = 0.033673469389

Calculate the square root of the right side: 0.183503323

Break this problem into two subproblems by setting 
(x + -0.07142857145) equal to 0.183503323 and -0.183503323.

Subproblem 1
x + -0.07142857145 = 0.183503323

Simplifying
x + -0.07142857145 = 0.183503323

Reorder the terms:
-0.07142857145 + x = 0.183503323

Solving
-0.07142857145 + x = 0.183503323

Solving for variable 'x'.

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

Add '0.07142857145' to each side of the equation.
-0.07142857145 + 0.07142857145 + x = 0.183503323 + 0.07142857145

Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000
0.00000000000 + x = 0.183503323 + 0.07142857145
x = 0.183503323 + 0.07142857145

Combine like terms: 0.183503323 + 0.07142857145 = 0.25493189445
x = 0.25493189445

Simplifying
x = 0.25493189445

Subproblem 2
x + -0.07142857145 = -0.183503323

Simplifying
x + -0.07142857145 = -0.183503323

Reorder the terms:
-0.07142857145 + x = -0.183503323

Solving
-0.07142857145 + x = -0.183503323

Solving for variable 'x'.

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

Add '0.07142857145' to each side of the equation.
-0.07142857145 + 0.07142857145 + x = -0.183503323 + 0.07142857145

Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000
0.00000000000 + x = -0.183503323 + 0.07142857145
x = -0.183503323 + 0.07142857145

Combine like terms: -0.183503323 + 0.07142857145 = -0.11207475155
x = -0.11207475155

Simplifying
x = -0.11207475155

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.25493189445, -0.11207475155}
Solution
x = {0.25493189445, -0.11207475155}