50+x(75+2x)=0

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Solution for 50+x(75+2x)=0 equation: 


Simplifying
50 + x(75 + 2x) = 0
50 + (75 * x + 2x * x) = 0
50 + (75x + 2x2) = 0

Solving
50 + 75x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
25 + 37.5x + x2 = 0

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + 37.5x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + 37.5x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 37.5x + x2 = 0 + -25
37.5x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
37.5x + x2 = -25

The x term is 37.5x.  Take half its coefficient (18.75).
Square it (351.5625) and add it to both sides.

Add '351.5625' to each side of the equation.
37.5x + 351.5625 + x2 = -25 + 351.5625

Reorder the terms:
351.5625 + 37.5x + x2 = -25 + 351.5625

Combine like terms: -25 + 351.5625 = 326.5625
351.5625 + 37.5x + x2 = 326.5625

Factor a perfect square on the left side:
(x + 18.75)(x + 18.75) = 326.5625

Calculate the square root of the right side: 18.071040369

Break this problem into two subproblems by setting 
(x + 18.75) equal to 18.071040369 and -18.071040369.


Subproblem 1
x + 18.75 = 18.071040369

Simplifying
x + 18.75 = 18.071040369

Reorder the terms:
18.75 + x = 18.071040369

Solving
18.75 + x = 18.071040369

Solving for variable 'x'.

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

Add '-18.75' to each side of the equation.
18.75 + -18.75 + x = 18.071040369 + -18.75

Combine like terms: 18.75 + -18.75 = 0.00
0.00 + x = 18.071040369 + -18.75
x = 18.071040369 + -18.75

Combine like terms: 18.071040369 + -18.75 = -0.678959631
x = -0.678959631

Simplifying
x = -0.678959631


Subproblem 2
x + 18.75 = -18.071040369

Simplifying
x + 18.75 = -18.071040369

Reorder the terms:
18.75 + x = -18.071040369

Solving
18.75 + x = -18.071040369

Solving for variable 'x'.

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

Add '-18.75' to each side of the equation.
18.75 + -18.75 + x = -18.071040369 + -18.75

Combine like terms: 18.75 + -18.75 = 0.00
0.00 + x = -18.071040369 + -18.75
x = -18.071040369 + -18.75

Combine like terms: -18.071040369 + -18.75 = -36.821040369
x = -36.821040369

Simplifying
x = -36.821040369


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.678959631, -36.821040369}

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