2x(x+7)=500

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Solution for 2x(x+7)=500 equation: 


Simplifying
2x(x + 7) = 500

Reorder the terms:
2x(7 + x) = 500
(7 * 2x + x * 2x) = 500
(14x + 2x2) = 500

Solving
14x + 2x2 = 500

Solving for variable 'x'.

Reorder the terms:
-500 + 14x + 2x2 = 500 + -500

Combine like terms: 500 + -500 = 0
-500 + 14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-250 + 7x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-250 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-250 + 7x + x2 = 0

Solving
-250 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '250' to each side of the equation.
-250 + 7x + 250 + x2 = 0 + 250

Reorder the terms:
-250 + 250 + 7x + x2 = 0 + 250

Combine like terms: -250 + 250 = 0
0 + 7x + x2 = 0 + 250
7x + x2 = 0 + 250

Combine like terms: 0 + 250 = 250
7x + x2 = 250

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 250 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 250 + 12.25

Combine like terms: 250 + 12.25 = 262.25
12.25 + 7x + x2 = 262.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 262.25

Calculate the square root of the right side: 16.194134741

Break this problem into two subproblems by setting 
(x + 3.5) equal to 16.194134741 and -16.194134741.


Subproblem 1
x + 3.5 = 16.194134741

Simplifying
x + 3.5 = 16.194134741

Reorder the terms:
3.5 + x = 16.194134741

Solving
3.5 + x = 16.194134741

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 16.194134741 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 16.194134741 + -3.5
x = 16.194134741 + -3.5

Combine like terms: 16.194134741 + -3.5 = 12.694134741
x = 12.694134741

Simplifying
x = 12.694134741


Subproblem 2
x + 3.5 = -16.194134741

Simplifying
x + 3.5 = -16.194134741

Reorder the terms:
3.5 + x = -16.194134741

Solving
3.5 + x = -16.194134741

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -16.194134741 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -16.194134741 + -3.5
x = -16.194134741 + -3.5

Combine like terms: -16.194134741 + -3.5 = -19.694134741
x = -19.694134741

Simplifying
x = -19.694134741


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.694134741, -19.694134741}
Solution
x = {12.694134741, -19.694134741}

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