x(x+13)=18

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Solution for x(x+13)=18 equation:


Simplifying
x(x + 13) = 18

Reorder the terms:
x(13 + x) = 18
(13 * x + x * x) = 18
(13x + x2) = 18

Solving
13x + x2 = 18

Solving for variable 'x'.

Reorder the terms:
-18 + 13x + x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 13x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 13x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 13x + x2 = 0 + 18
13x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
13x + x2 = 18

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 18 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 18 + 42.25

Combine like terms: 18 + 42.25 = 60.25
42.25 + 13x + x2 = 60.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(x + 6.5) equal to 7.762087348 and -7.762087348.

Subproblem 1

x + 6.5 = 7.762087348 Simplifying x + 6.5 = 7.762087348 Reorder the terms: 6.5 + x = 7.762087348 Solving 6.5 + x = 7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 7.762087348 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 7.762087348 + -6.5 x = 7.762087348 + -6.5 Combine like terms: 7.762087348 + -6.5 = 1.262087348 x = 1.262087348 Simplifying x = 1.262087348

Subproblem 2

x + 6.5 = -7.762087348 Simplifying x + 6.5 = -7.762087348 Reorder the terms: 6.5 + x = -7.762087348 Solving 6.5 + x = -7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -7.762087348 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -7.762087348 + -6.5 x = -7.762087348 + -6.5 Combine like terms: -7.762087348 + -6.5 = -14.262087348 x = -14.262087348 Simplifying x = -14.262087348

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.262087348, -14.262087348}

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