(x+30)x*20=5000

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Solution for (x+30)x*20=5000 equation: 


Simplifying
(x + 30) * x * 20 = 5000

Reorder the terms:
(30 + x) * x * 20 = 5000

Reorder the terms for easier multiplication:
20x(30 + x) = 5000
(30 * 20x + x * 20x) = 5000
(600x + 20x2) = 5000

Solving
600x + 20x2 = 5000

Solving for variable 'x'.

Reorder the terms:
-5000 + 600x + 20x2 = 5000 + -5000

Combine like terms: 5000 + -5000 = 0
-5000 + 600x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '20'.
20(-250 + 30x + x2) = 0

Ignore the factor 20.

Subproblem 1
Set the factor '(-250 + 30x + x2)' equal to zero and attempt to solve:

Simplifying
-250 + 30x + x2 = 0

Solving
-250 + 30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '250' to each side of the equation.
-250 + 30x + 250 + x2 = 0 + 250

Reorder the terms:
-250 + 250 + 30x + x2 = 0 + 250

Combine like terms: -250 + 250 = 0
0 + 30x + x2 = 0 + 250
30x + x2 = 0 + 250

Combine like terms: 0 + 250 = 250
30x + x2 = 250

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = 250 + 225

Reorder the terms:
225 + 30x + x2 = 250 + 225

Combine like terms: 250 + 225 = 475
225 + 30x + x2 = 475

Factor a perfect square on the left side:
(x + 15)(x + 15) = 475

Calculate the square root of the right side: 21.794494718

Break this problem into two subproblems by setting 
(x + 15) equal to 21.794494718 and -21.794494718.


Subproblem 1
x + 15 = 21.794494718

Simplifying
x + 15 = 21.794494718

Reorder the terms:
15 + x = 21.794494718

Solving
15 + x = 21.794494718

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 21.794494718 + -15

Combine like terms: 15 + -15 = 0
0 + x = 21.794494718 + -15
x = 21.794494718 + -15

Combine like terms: 21.794494718 + -15 = 6.794494718
x = 6.794494718

Simplifying
x = 6.794494718


Subproblem 2
x + 15 = -21.794494718

Simplifying
x + 15 = -21.794494718

Reorder the terms:
15 + x = -21.794494718

Solving
15 + x = -21.794494718

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -21.794494718 + -15

Combine like terms: 15 + -15 = 0
0 + x = -21.794494718 + -15
x = -21.794494718 + -15

Combine like terms: -21.794494718 + -15 = -36.794494718
x = -36.794494718

Simplifying
x = -36.794494718


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.794494718, -36.794494718}
Solution
x = {6.794494718, -36.794494718}

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