26x(x+2)=8320

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Solution for 26x(x+2)=8320 equation: 


Simplifying
26x(x + 2) = 8320

Reorder the terms:
26x(2 + x) = 8320
(2 * 26x + x * 26x) = 8320
(52x + 26x2) = 8320

Solving
52x + 26x2 = 8320

Solving for variable 'x'.

Reorder the terms:
-8320 + 52x + 26x2 = 8320 + -8320

Combine like terms: 8320 + -8320 = 0
-8320 + 52x + 26x2 = 0

Factor out the Greatest Common Factor (GCF), '26'.
26(-320 + 2x + x2) = 0

Ignore the factor 26.

Subproblem 1
Set the factor '(-320 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-320 + 2x + x2 = 0

Solving
-320 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '320' to each side of the equation.
-320 + 2x + 320 + x2 = 0 + 320

Reorder the terms:
-320 + 320 + 2x + x2 = 0 + 320

Combine like terms: -320 + 320 = 0
0 + 2x + x2 = 0 + 320
2x + x2 = 0 + 320

Combine like terms: 0 + 320 = 320
2x + x2 = 320

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 320 + 1

Reorder the terms:
1 + 2x + x2 = 320 + 1

Combine like terms: 320 + 1 = 321
1 + 2x + x2 = 321

Factor a perfect square on the left side:
(x + 1)(x + 1) = 321

Calculate the square root of the right side: 17.916472867

Break this problem into two subproblems by setting 
(x + 1) equal to 17.916472867 and -17.916472867.


Subproblem 1
x + 1 = 17.916472867

Simplifying
x + 1 = 17.916472867

Reorder the terms:
1 + x = 17.916472867

Solving
1 + x = 17.916472867

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 17.916472867 + -1

Combine like terms: 1 + -1 = 0
0 + x = 17.916472867 + -1
x = 17.916472867 + -1

Combine like terms: 17.916472867 + -1 = 16.916472867
x = 16.916472867

Simplifying
x = 16.916472867


Subproblem 2
x + 1 = -17.916472867

Simplifying
x + 1 = -17.916472867

Reorder the terms:
1 + x = -17.916472867

Solving
1 + x = -17.916472867

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -17.916472867 + -1

Combine like terms: 1 + -1 = 0
0 + x = -17.916472867 + -1
x = -17.916472867 + -1

Combine like terms: -17.916472867 + -1 = -18.916472867
x = -18.916472867

Simplifying
x = -18.916472867


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.916472867, -18.916472867}
Solution
x = {16.916472867, -18.916472867}

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