13x(x+36)=5

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Solution for 13x(x+36)=5 equation:


Simplifying
13x(x + 36) = 5

Reorder the terms:
13x(36 + x) = 5
(36 * 13x + x * 13x) = 5
(468x + 13x2) = 5

Solving
468x + 13x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + 468x + 13x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 468x + 13x2 = 0

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

Divide each side by '13'.
-0.3846153846 + 36x + x2 = 0

Move the constant term to the right:

Add '0.3846153846' to each side of the equation.
-0.3846153846 + 36x + 0.3846153846 + x2 = 0 + 0.3846153846

Reorder the terms:
-0.3846153846 + 0.3846153846 + 36x + x2 = 0 + 0.3846153846

Combine like terms: -0.3846153846 + 0.3846153846 = 0.0000000000
0.0000000000 + 36x + x2 = 0 + 0.3846153846
36x + x2 = 0 + 0.3846153846

Combine like terms: 0 + 0.3846153846 = 0.3846153846
36x + x2 = 0.3846153846

The x term is 36x.  Take half its coefficient (18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
36x + 324 + x2 = 0.3846153846 + 324

Reorder the terms:
324 + 36x + x2 = 0.3846153846 + 324

Combine like terms: 0.3846153846 + 324 = 324.3846153846
324 + 36x + x2 = 324.3846153846

Factor a perfect square on the left side:
(x + 18)(x + 18) = 324.3846153846

Calculate the square root of the right side: 18.010680592

Break this problem into two subproblems by setting 
(x + 18) equal to 18.010680592 and -18.010680592.

Subproblem 1

x + 18 = 18.010680592 Simplifying x + 18 = 18.010680592 Reorder the terms: 18 + x = 18.010680592 Solving 18 + x = 18.010680592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 18.010680592 + -18 Combine like terms: 18 + -18 = 0 0 + x = 18.010680592 + -18 x = 18.010680592 + -18 Combine like terms: 18.010680592 + -18 = 0.010680592 x = 0.010680592 Simplifying x = 0.010680592

Subproblem 2

x + 18 = -18.010680592 Simplifying x + 18 = -18.010680592 Reorder the terms: 18 + x = -18.010680592 Solving 18 + x = -18.010680592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -18.010680592 + -18 Combine like terms: 18 + -18 = 0 0 + x = -18.010680592 + -18 x = -18.010680592 + -18 Combine like terms: -18.010680592 + -18 = -36.010680592 x = -36.010680592 Simplifying x = -36.010680592

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.010680592, -36.010680592}

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