0.1(x+50)0.7x=21

Solution for 0.1(x+50)0.7x=21 equation:

Simplifying
0.1(x + 50) * 0.7x = 21

Reorder the terms:
0.1(50 + x) * 0.7x = 21

Reorder the terms for easier multiplication:
0.1 * 0.7x(50 + x) = 21

Multiply 0.1 * 0.7
0.07x(50 + x) = 21
(50 * 0.07x + x * 0.07x) = 21
(3.5x + 0.07x2) = 21

Solving
3.5x + 0.07x2 = 21

Solving for variable 'x'.

Reorder the terms:
-21 + 3.5x + 0.07x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + 3.5x + 0.07x2 = 0

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

Divide each side by '0.07'.
-300 + 50x + x2 = 0

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + 50x + 300 + x2 = 0 + 300

Reorder the terms:
-300 + 300 + 50x + x2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + 50x + x2 = 0 + 300
50x + x2 = 0 + 300

Combine like terms: 0 + 300 = 300
50x + x2 = 300

The x term is 50x.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50x + 625 + x2 = 300 + 625

Reorder the terms:
625 + 50x + x2 = 300 + 625

Combine like terms: 300 + 625 = 925
625 + 50x + x2 = 925

Factor a perfect square on the left side:
(x + 25)(x + 25) = 925

Calculate the square root of the right side: 30.413812651

Break this problem into two subproblems by setting 
(x + 25) equal to 30.413812651 and -30.413812651.

Subproblem 1
x + 25 = 30.413812651

Simplifying
x + 25 = 30.413812651

Reorder the terms:
25 + x = 30.413812651

Solving
25 + x = 30.413812651

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = 30.413812651 + -25

Combine like terms: 25 + -25 = 0
0 + x = 30.413812651 + -25
x = 30.413812651 + -25

Combine like terms: 30.413812651 + -25 = 5.413812651
x = 5.413812651

Simplifying
x = 5.413812651

Subproblem 2
x + 25 = -30.413812651

Simplifying
x + 25 = -30.413812651

Reorder the terms:
25 + x = -30.413812651

Solving
25 + x = -30.413812651

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = -30.413812651 + -25

Combine like terms: 25 + -25 = 0
0 + x = -30.413812651 + -25
x = -30.413812651 + -25

Combine like terms: -30.413812651 + -25 = -55.413812651
x = -55.413812651

Simplifying
x = -55.413812651

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.413812651, -55.413812651}