2x(x+48)=500

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Solution for 2x(x+48)=500 equation: 


Simplifying
2x(x + 48) = 500

Reorder the terms:
2x(48 + x) = 500
(48 * 2x + x * 2x) = 500
(96x + 2x2) = 500

Solving
96x + 2x2 = 500

Solving for variable 'x'.

Reorder the terms:
-500 + 96x + 2x2 = 500 + -500

Combine like terms: 500 + -500 = 0
-500 + 96x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-250 + 48x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-250 + 48x + x2)' equal to zero and attempt to solve:

Simplifying
-250 + 48x + x2 = 0

Solving
-250 + 48x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '250' to each side of the equation.
-250 + 48x + 250 + x2 = 0 + 250

Reorder the terms:
-250 + 250 + 48x + x2 = 0 + 250

Combine like terms: -250 + 250 = 0
0 + 48x + x2 = 0 + 250
48x + x2 = 0 + 250

Combine like terms: 0 + 250 = 250
48x + x2 = 250

The x term is 48x.  Take half its coefficient (24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
48x + 576 + x2 = 250 + 576

Reorder the terms:
576 + 48x + x2 = 250 + 576

Combine like terms: 250 + 576 = 826
576 + 48x + x2 = 826

Factor a perfect square on the left side:
(x + 24)(x + 24) = 826

Calculate the square root of the right side: 28.740215726

Break this problem into two subproblems by setting 
(x + 24) equal to 28.740215726 and -28.740215726.


Subproblem 1
x + 24 = 28.740215726

Simplifying
x + 24 = 28.740215726

Reorder the terms:
24 + x = 28.740215726

Solving
24 + x = 28.740215726

Solving for variable 'x'.

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

Add '-24' to each side of the equation.
24 + -24 + x = 28.740215726 + -24

Combine like terms: 24 + -24 = 0
0 + x = 28.740215726 + -24
x = 28.740215726 + -24

Combine like terms: 28.740215726 + -24 = 4.740215726
x = 4.740215726

Simplifying
x = 4.740215726


Subproblem 2
x + 24 = -28.740215726

Simplifying
x + 24 = -28.740215726

Reorder the terms:
24 + x = -28.740215726

Solving
24 + x = -28.740215726

Solving for variable 'x'.

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

Add '-24' to each side of the equation.
24 + -24 + x = -28.740215726 + -24

Combine like terms: 24 + -24 = 0
0 + x = -28.740215726 + -24
x = -28.740215726 + -24

Combine like terms: -28.740215726 + -24 = -52.740215726
x = -52.740215726

Simplifying
x = -52.740215726


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.740215726, -52.740215726}
Solution
x = {4.740215726, -52.740215726}

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