(7x+1)(7x+1)+5=10

Solution for (7x+1)(7x+1)+5=10 equation:

Simplifying
(7x + 1)(7x + 1) + 5 = 10

Reorder the terms:
(1 + 7x)(7x + 1) + 5 = 10

Reorder the terms:
(1 + 7x)(1 + 7x) + 5 = 10

Multiply (1 + 7x) * (1 + 7x)
(1(1 + 7x) + 7x * (1 + 7x)) + 5 = 10
((1 * 1 + 7x * 1) + 7x * (1 + 7x)) + 5 = 10
((1 + 7x) + 7x * (1 + 7x)) + 5 = 10
(1 + 7x + (1 * 7x + 7x * 7x)) + 5 = 10
(1 + 7x + (7x + 49x2)) + 5 = 10

Combine like terms: 7x + 7x = 14x
(1 + 14x + 49x2) + 5 = 10

Reorder the terms:
1 + 5 + 14x + 49x2 = 10

Combine like terms: 1 + 5 = 6
6 + 14x + 49x2 = 10

Solving
6 + 14x + 49x2 = 10

Solving for variable 'x'.

Reorder the terms:
6 + -10 + 14x + 49x2 = 10 + -10

Combine like terms: 6 + -10 = -4
-4 + 14x + 49x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-4 + 14x + 49x2 = 0

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

Divide each side by '49'.
-0.08163265306 + 0.2857142857x + x2 = 0

Move the constant term to the right:

Add '0.08163265306' to each side of the equation.
-0.08163265306 + 0.2857142857x + 0.08163265306 + x2 = 0 + 0.08163265306

Reorder the terms:
-0.08163265306 + 0.08163265306 + 0.2857142857x + x2 = 0 + 0.08163265306

Combine like terms: -0.08163265306 + 0.08163265306 = 0.00000000000
0.00000000000 + 0.2857142857x + x2 = 0 + 0.08163265306
0.2857142857x + x2 = 0 + 0.08163265306

Combine like terms: 0 + 0.08163265306 = 0.08163265306
0.2857142857x + x2 = 0.08163265306

The x term is 0.2857142857x.  Take half its coefficient (0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
0.2857142857x + 0.02040816328 + x2 = 0.08163265306 + 0.02040816328

Reorder the terms:
0.02040816328 + 0.2857142857x + x2 = 0.08163265306 + 0.02040816328

Combine like terms: 0.08163265306 + 0.02040816328 = 0.10204081634
0.02040816328 + 0.2857142857x + x2 = 0.10204081634

Factor a perfect square on the left side:
(x + 0.1428571429)(x + 0.1428571429) = 0.10204081634

Calculate the square root of the right side: 0.319438283

Break this problem into two subproblems by setting 
(x + 0.1428571429) equal to 0.319438283 and -0.319438283.

Subproblem 1
x + 0.1428571429 = 0.319438283

Simplifying
x + 0.1428571429 = 0.319438283

Reorder the terms:
0.1428571429 + x = 0.319438283

Solving
0.1428571429 + x = 0.319438283

Solving for variable 'x'.

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

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -0.1428571429 + x = 0.319438283 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + x = 0.319438283 + -0.1428571429
x = 0.319438283 + -0.1428571429

Combine like terms: 0.319438283 + -0.1428571429 = 0.1765811401
x = 0.1765811401

Simplifying
x = 0.1765811401

Subproblem 2
x + 0.1428571429 = -0.319438283

Simplifying
x + 0.1428571429 = -0.319438283

Reorder the terms:
0.1428571429 + x = -0.319438283

Solving
0.1428571429 + x = -0.319438283

Solving for variable 'x'.

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

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -0.1428571429 + x = -0.319438283 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + x = -0.319438283 + -0.1428571429
x = -0.319438283 + -0.1428571429

Combine like terms: -0.319438283 + -0.1428571429 = -0.4622954259
x = -0.4622954259

Simplifying
x = -0.4622954259

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1765811401, -0.4622954259}