71.4=(848+72x)(12+x)

Solution for 71.4=(848+72x)(12+x) equation:

Simplifying
71.4 = (848 + 72x)(12 + x)

Multiply (848 + 72x) * (12 + x)
71.4 = (848(12 + x) + 72x * (12 + x))
71.4 = ((12 * 848 + x * 848) + 72x * (12 + x))
71.4 = ((10176 + 848x) + 72x * (12 + x))
71.4 = (10176 + 848x + (12 * 72x + x * 72x))
71.4 = (10176 + 848x + (864x + 72x2))

Combine like terms: 848x + 864x = 1712x
71.4 = (10176 + 1712x + 72x2)

Solving
71.4 = 10176 + 1712x + 72x2

Solving for variable 'x'.

Combine like terms: 71.4 + -10176 = -10104.6
-10104.6 + -1712x + -72x2 = 10176 + 1712x + 72x2 + -10176 + -1712x + -72x2

Reorder the terms:
-10104.6 + -1712x + -72x2 = 10176 + -10176 + 1712x + -1712x + 72x2 + -72x2

Combine like terms: 10176 + -10176 = 0
-10104.6 + -1712x + -72x2 = 0 + 1712x + -1712x + 72x2 + -72x2
-10104.6 + -1712x + -72x2 = 1712x + -1712x + 72x2 + -72x2

Combine like terms: 1712x + -1712x = 0
-10104.6 + -1712x + -72x2 = 0 + 72x2 + -72x2
-10104.6 + -1712x + -72x2 = 72x2 + -72x2

Combine like terms: 72x2 + -72x2 = 0
-10104.6 + -1712x + -72x2 = 0

Begin completing the square.  Divide all terms by
-72 the coefficient of the squared term: 

Divide each side by '-72'.
140.3416667 + 23.77777778x + x2 = 0

Move the constant term to the right:

Add '-140.3416667' to each side of the equation.
140.3416667 + 23.77777778x + -140.3416667 + x2 = 0 + -140.3416667

Reorder the terms:
140.3416667 + -140.3416667 + 23.77777778x + x2 = 0 + -140.3416667

Combine like terms: 140.3416667 + -140.3416667 = 0.0000000
0.0000000 + 23.77777778x + x2 = 0 + -140.3416667
23.77777778x + x2 = 0 + -140.3416667

Combine like terms: 0 + -140.3416667 = -140.3416667
23.77777778x + x2 = -140.3416667

The x term is 23.77777778x.  Take half its coefficient (11.88888889).
Square it (141.3456790) and add it to both sides.

Add '141.3456790' to each side of the equation.
23.77777778x + 141.3456790 + x2 = -140.3416667 + 141.3456790

Reorder the terms:
141.3456790 + 23.77777778x + x2 = -140.3416667 + 141.3456790

Combine like terms: -140.3416667 + 141.3456790 = 1.0040123
141.3456790 + 23.77777778x + x2 = 1.0040123

Factor a perfect square on the left side:
(x + 11.88888889)(x + 11.88888889) = 1.0040123

Calculate the square root of the right side: 1.002004142

Break this problem into two subproblems by setting 
(x + 11.88888889) equal to 1.002004142 and -1.002004142.

Subproblem 1
x + 11.88888889 = 1.002004142

Simplifying
x + 11.88888889 = 1.002004142

Reorder the terms:
11.88888889 + x = 1.002004142

Solving
11.88888889 + x = 1.002004142

Solving for variable 'x'.

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

Add '-11.88888889' to each side of the equation.
11.88888889 + -11.88888889 + x = 1.002004142 + -11.88888889

Combine like terms: 11.88888889 + -11.88888889 = 0.00000000
0.00000000 + x = 1.002004142 + -11.88888889
x = 1.002004142 + -11.88888889

Combine like terms: 1.002004142 + -11.88888889 = -10.886884748
x = -10.886884748

Simplifying
x = -10.886884748

Subproblem 2
x + 11.88888889 = -1.002004142

Simplifying
x + 11.88888889 = -1.002004142

Reorder the terms:
11.88888889 + x = -1.002004142

Solving
11.88888889 + x = -1.002004142

Solving for variable 'x'.

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

Add '-11.88888889' to each side of the equation.
11.88888889 + -11.88888889 + x = -1.002004142 + -11.88888889

Combine like terms: 11.88888889 + -11.88888889 = 0.00000000
0.00000000 + x = -1.002004142 + -11.88888889
x = -1.002004142 + -11.88888889

Combine like terms: -1.002004142 + -11.88888889 = -12.890893032
x = -12.890893032

Simplifying
x = -12.890893032

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-10.886884748, -12.890893032}