5x*(x+50)=29950

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Solution for 5x*(x+50)=29950 equation: 


Simplifying
5x(x + 50) = 29950

Reorder the terms:
5x(50 + x) = 29950
(50 * 5x + x * 5x) = 29950
(250x + 5x2) = 29950

Solving
250x + 5x2 = 29950

Solving for variable 'x'.

Reorder the terms:
-29950 + 250x + 5x2 = 29950 + -29950

Combine like terms: 29950 + -29950 = 0
-29950 + 250x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-5990 + 50x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-5990 + 50x + x2)' equal to zero and attempt to solve:

Simplifying
-5990 + 50x + x2 = 0

Solving
-5990 + 50x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5990' to each side of the equation.
-5990 + 50x + 5990 + x2 = 0 + 5990

Reorder the terms:
-5990 + 5990 + 50x + x2 = 0 + 5990

Combine like terms: -5990 + 5990 = 0
0 + 50x + x2 = 0 + 5990
50x + x2 = 0 + 5990

Combine like terms: 0 + 5990 = 5990
50x + x2 = 5990

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 = 5990 + 625

Reorder the terms:
625 + 50x + x2 = 5990 + 625

Combine like terms: 5990 + 625 = 6615
625 + 50x + x2 = 6615

Factor a perfect square on the left side:
(x + 25)(x + 25) = 6615

Calculate the square root of the right side: 81.33265027

Break this problem into two subproblems by setting 
(x + 25) equal to 81.33265027 and -81.33265027.


Subproblem 1
x + 25 = 81.33265027

Simplifying
x + 25 = 81.33265027

Reorder the terms:
25 + x = 81.33265027

Solving
25 + x = 81.33265027

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 = 81.33265027 + -25

Combine like terms: 25 + -25 = 0
0 + x = 81.33265027 + -25
x = 81.33265027 + -25

Combine like terms: 81.33265027 + -25 = 56.33265027
x = 56.33265027

Simplifying
x = 56.33265027


Subproblem 2
x + 25 = -81.33265027

Simplifying
x + 25 = -81.33265027

Reorder the terms:
25 + x = -81.33265027

Solving
25 + x = -81.33265027

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 = -81.33265027 + -25

Combine like terms: 25 + -25 = 0
0 + x = -81.33265027 + -25
x = -81.33265027 + -25

Combine like terms: -81.33265027 + -25 = -106.33265027
x = -106.33265027

Simplifying
x = -106.33265027


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {56.33265027, -106.33265027}
Solution
x = {56.33265027, -106.33265027}

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