2x(x+7)=250

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Solution for 2x(x+7)=250 equation: 


Simplifying
2x(x + 7) = 250

Reorder the terms:
2x(7 + x) = 250
(7 * 2x + x * 2x) = 250
(14x + 2x2) = 250

Solving
14x + 2x2 = 250

Solving for variable 'x'.

Reorder the terms:
-250 + 14x + 2x2 = 250 + -250

Combine like terms: 250 + -250 = 0
-250 + 14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-125 + 7x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-125 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-125 + 7x + x2 = 0

Solving
-125 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '125' to each side of the equation.
-125 + 7x + 125 + x2 = 0 + 125

Reorder the terms:
-125 + 125 + 7x + x2 = 0 + 125

Combine like terms: -125 + 125 = 0
0 + 7x + x2 = 0 + 125
7x + x2 = 0 + 125

Combine like terms: 0 + 125 = 125
7x + x2 = 125

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 = 125 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 125 + 12.25

Combine like terms: 125 + 12.25 = 137.25
12.25 + 7x + x2 = 137.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 137.25

Calculate the square root of the right side: 11.715374514

Break this problem into two subproblems by setting 
(x + 3.5) equal to 11.715374514 and -11.715374514.


Subproblem 1
x + 3.5 = 11.715374514

Simplifying
x + 3.5 = 11.715374514

Reorder the terms:
3.5 + x = 11.715374514

Solving
3.5 + x = 11.715374514

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 = 11.715374514 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 11.715374514 + -3.5
x = 11.715374514 + -3.5

Combine like terms: 11.715374514 + -3.5 = 8.215374514
x = 8.215374514

Simplifying
x = 8.215374514


Subproblem 2
x + 3.5 = -11.715374514

Simplifying
x + 3.5 = -11.715374514

Reorder the terms:
3.5 + x = -11.715374514

Solving
3.5 + x = -11.715374514

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 = -11.715374514 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -11.715374514 + -3.5
x = -11.715374514 + -3.5

Combine like terms: -11.715374514 + -3.5 = -15.215374514
x = -15.215374514

Simplifying
x = -15.215374514


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.215374514, -15.215374514}
Solution
x = {8.215374514, -15.215374514}

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