2x(2x+13)=36

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Solution for 2x(2x+13)=36 equation: 


Simplifying
2x(2x + 13) = 36

Reorder the terms:
2x(13 + 2x) = 36
(13 * 2x + 2x * 2x) = 36
(26x + 4x2) = 36

Solving
26x + 4x2 = 36

Solving for variable 'x'.

Reorder the terms:
-36 + 26x + 4x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 26x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + 13x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-18 + 13x + 2x2)' equal to zero and attempt to solve:

Simplifying
-18 + 13x + 2x2 = 0

Solving
-18 + 13x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-9 + 6.5x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 6.5x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 6.5x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 6.5x + x2 = 0 + 9
6.5x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
6.5x + x2 = 9

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = 9 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = 9 + 10.5625

Combine like terms: 9 + 10.5625 = 19.5625
10.5625 + 6.5x + x2 = 19.5625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 19.5625

Calculate the square root of the right side: 4.422951503

Break this problem into two subproblems by setting 
(x + 3.25) equal to 4.422951503 and -4.422951503.


Subproblem 1
x + 3.25 = 4.422951503

Simplifying
x + 3.25 = 4.422951503

Reorder the terms:
3.25 + x = 4.422951503

Solving
3.25 + x = 4.422951503

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = 4.422951503 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = 4.422951503 + -3.25
x = 4.422951503 + -3.25

Combine like terms: 4.422951503 + -3.25 = 1.172951503
x = 1.172951503

Simplifying
x = 1.172951503


Subproblem 2
x + 3.25 = -4.422951503

Simplifying
x + 3.25 = -4.422951503

Reorder the terms:
3.25 + x = -4.422951503

Solving
3.25 + x = -4.422951503

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = -4.422951503 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = -4.422951503 + -3.25
x = -4.422951503 + -3.25

Combine like terms: -4.422951503 + -3.25 = -7.672951503
x = -7.672951503

Simplifying
x = -7.672951503


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.172951503, -7.672951503}
Solution
x = {1.172951503, -7.672951503}

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