2x(x+7)=82

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Solution for 2x(x+7)=82 equation: 


Simplifying
2x(x + 7) = 82

Reorder the terms:
2x(7 + x) = 82
(7 * 2x + x * 2x) = 82
(14x + 2x2) = 82

Solving
14x + 2x2 = 82

Solving for variable 'x'.

Reorder the terms:
-82 + 14x + 2x2 = 82 + -82

Combine like terms: 82 + -82 = 0
-82 + 14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-41 + 7x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-41 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-41 + 7x + x2 = 0

Solving
-41 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + 7x + 41 + x2 = 0 + 41

Reorder the terms:
-41 + 41 + 7x + x2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + 7x + x2 = 0 + 41
7x + x2 = 0 + 41

Combine like terms: 0 + 41 = 41
7x + x2 = 41

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 = 41 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 41 + 12.25

Combine like terms: 41 + 12.25 = 53.25
12.25 + 7x + x2 = 53.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 53.25

Calculate the square root of the right side: 7.29725976

Break this problem into two subproblems by setting 
(x + 3.5) equal to 7.29725976 and -7.29725976.


Subproblem 1
x + 3.5 = 7.29725976

Simplifying
x + 3.5 = 7.29725976

Reorder the terms:
3.5 + x = 7.29725976

Solving
3.5 + x = 7.29725976

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 = 7.29725976 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 7.29725976 + -3.5
x = 7.29725976 + -3.5

Combine like terms: 7.29725976 + -3.5 = 3.79725976
x = 3.79725976

Simplifying
x = 3.79725976


Subproblem 2
x + 3.5 = -7.29725976

Simplifying
x + 3.5 = -7.29725976

Reorder the terms:
3.5 + x = -7.29725976

Solving
3.5 + x = -7.29725976

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 = -7.29725976 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -7.29725976 + -3.5
x = -7.29725976 + -3.5

Combine like terms: -7.29725976 + -3.5 = -10.79725976
x = -10.79725976

Simplifying
x = -10.79725976


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.79725976, -10.79725976}
Solution
x = {3.79725976, -10.79725976}

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