50.4=2.5x*(15.4+x)

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Solution for 50.4=2.5x*(15.4+x) equation: 


Simplifying
50.4 = 2.5x(15.4 + x)
50.4 = (15.4 * 2.5x + x * 2.5x)
50.4 = (38.5x + 2.5x2)

Solving
50.4 = 38.5x + 2.5x2

Solving for variable 'x'.

Reorder the terms:
50.4 + -38.5x + -2.5x2 = 38.5x + -38.5x + 2.5x2 + -2.5x2

Combine like terms: 38.5x + -38.5x = 0.0
50.4 + -38.5x + -2.5x2 = 0.0 + 2.5x2 + -2.5x2
50.4 + -38.5x + -2.5x2 = 2.5x2 + -2.5x2

Combine like terms: 2.5x2 + -2.5x2 = 0.0
50.4 + -38.5x + -2.5x2 = 0.0

Begin completing the square.  Divide all terms by
-2.5 the coefficient of the squared term: 

Divide each side by '-2.5'.
-20.16 + 15.4x + x2 = 0

Move the constant term to the right:

Add '20.16' to each side of the equation.
-20.16 + 15.4x + 20.16 + x2 = 0 + 20.16

Reorder the terms:
-20.16 + 20.16 + 15.4x + x2 = 0 + 20.16

Combine like terms: -20.16 + 20.16 = 0.00
0.00 + 15.4x + x2 = 0 + 20.16
15.4x + x2 = 0 + 20.16

Combine like terms: 0 + 20.16 = 20.16
15.4x + x2 = 20.16

The x term is 15.4x.  Take half its coefficient (7.7).
Square it (59.29) and add it to both sides.

Add '59.29' to each side of the equation.
15.4x + 59.29 + x2 = 20.16 + 59.29

Reorder the terms:
59.29 + 15.4x + x2 = 20.16 + 59.29

Combine like terms: 20.16 + 59.29 = 79.45
59.29 + 15.4x + x2 = 79.45

Factor a perfect square on the left side:
(x + 7.7)(x + 7.7) = 79.45

Calculate the square root of the right side: 8.913472948

Break this problem into two subproblems by setting 
(x + 7.7) equal to 8.913472948 and -8.913472948.


Subproblem 1
x + 7.7 = 8.913472948

Simplifying
x + 7.7 = 8.913472948

Reorder the terms:
7.7 + x = 8.913472948

Solving
7.7 + x = 8.913472948

Solving for variable 'x'.

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

Add '-7.7' to each side of the equation.
7.7 + -7.7 + x = 8.913472948 + -7.7

Combine like terms: 7.7 + -7.7 = 0.0
0.0 + x = 8.913472948 + -7.7
x = 8.913472948 + -7.7

Combine like terms: 8.913472948 + -7.7 = 1.213472948
x = 1.213472948

Simplifying
x = 1.213472948


Subproblem 2
x + 7.7 = -8.913472948

Simplifying
x + 7.7 = -8.913472948

Reorder the terms:
7.7 + x = -8.913472948

Solving
7.7 + x = -8.913472948

Solving for variable 'x'.

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

Add '-7.7' to each side of the equation.
7.7 + -7.7 + x = -8.913472948 + -7.7

Combine like terms: 7.7 + -7.7 = 0.0
0.0 + x = -8.913472948 + -7.7
x = -8.913472948 + -7.7

Combine like terms: -8.913472948 + -7.7 = -16.613472948
x = -16.613472948

Simplifying
x = -16.613472948


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.213472948, -16.613472948}

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