x+x+x(x+2)=360

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Solution for x+x+x(x+2)=360 equation:


Simplifying
x + x + x(x + 2) = 360

Reorder the terms:
x + x + x(2 + x) = 360
x + x + (2 * x + x * x) = 360
x + x + (2x + x2) = 360

Combine like terms: x + x = 2x
2x + 2x + x2 = 360

Combine like terms: 2x + 2x = 4x
4x + x2 = 360

Solving
4x + x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + 4x + x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '360' to each side of the equation.
-360 + 4x + 360 + x2 = 0 + 360

Reorder the terms:
-360 + 360 + 4x + x2 = 0 + 360

Combine like terms: -360 + 360 = 0
0 + 4x + x2 = 0 + 360
4x + x2 = 0 + 360

Combine like terms: 0 + 360 = 360
4x + x2 = 360

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 360 + 4

Reorder the terms:
4 + 4x + x2 = 360 + 4

Combine like terms: 360 + 4 = 364
4 + 4x + x2 = 364

Factor a perfect square on the left side:
(x + 2)(x + 2) = 364

Calculate the square root of the right side: 19.078784028

Break this problem into two subproblems by setting 
(x + 2) equal to 19.078784028 and -19.078784028.

Subproblem 1

x + 2 = 19.078784028 Simplifying x + 2 = 19.078784028 Reorder the terms: 2 + x = 19.078784028 Solving 2 + x = 19.078784028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 19.078784028 + -2 Combine like terms: 2 + -2 = 0 0 + x = 19.078784028 + -2 x = 19.078784028 + -2 Combine like terms: 19.078784028 + -2 = 17.078784028 x = 17.078784028 Simplifying x = 17.078784028

Subproblem 2

x + 2 = -19.078784028 Simplifying x + 2 = -19.078784028 Reorder the terms: 2 + x = -19.078784028 Solving 2 + x = -19.078784028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -19.078784028 + -2 Combine like terms: 2 + -2 = 0 0 + x = -19.078784028 + -2 x = -19.078784028 + -2 Combine like terms: -19.078784028 + -2 = -21.078784028 x = -21.078784028 Simplifying x = -21.078784028

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.078784028, -21.078784028}

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