36=(x+2)x

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


Simplifying
36 = (x + 2) * x

Reorder the terms:
36 = (2 + x) * x

Reorder the terms for easier multiplication:
36 = x(2 + x)
36 = (2 * x + x * x)
36 = (2x + x2)

Solving
36 = 2x + x2

Solving for variable 'x'.

Reorder the terms:
36 + -2x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
36 + -2x + -1x2 = 0 + x2 + -1x2
36 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
36 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-36 + 2x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 2x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 2x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 2x + x2 = 0 + 36
2x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
2x + x2 = 36

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 = 36 + 1

Reorder the terms:
1 + 2x + x2 = 36 + 1

Combine like terms: 36 + 1 = 37
1 + 2x + x2 = 37

Factor a perfect square on the left side:
(x + 1)(x + 1) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(x + 1) equal to 6.08276253 and -6.08276253.

Subproblem 1

x + 1 = 6.08276253 Simplifying x + 1 = 6.08276253 Reorder the terms: 1 + x = 6.08276253 Solving 1 + x = 6.08276253 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 = 6.08276253 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.08276253 + -1 x = 6.08276253 + -1 Combine like terms: 6.08276253 + -1 = 5.08276253 x = 5.08276253 Simplifying x = 5.08276253

Subproblem 2

x + 1 = -6.08276253 Simplifying x + 1 = -6.08276253 Reorder the terms: 1 + x = -6.08276253 Solving 1 + x = -6.08276253 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 = -6.08276253 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.08276253 + -1 x = -6.08276253 + -1 Combine like terms: -6.08276253 + -1 = -7.08276253 x = -7.08276253 Simplifying x = -7.08276253

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.08276253, -7.08276253}

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