x+x+x(x+2)=48

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Solution for x+x+x(x+2)=48 equation:


Simplifying
x + x + x(x + 2) = 48

Reorder the terms:
x + x + x(2 + x) = 48
x + x + (2 * x + x * x) = 48
x + x + (2x + x2) = 48

Combine like terms: x + x = 2x
2x + 2x + x2 = 48

Combine like terms: 2x + 2x = 4x
4x + x2 = 48

Solving
4x + x2 = 48

Solving for variable 'x'.

Reorder the terms:
-48 + 4x + x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 4x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 4x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 4x + x2 = 0 + 48
4x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
4x + x2 = 48

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 = 48 + 4

Reorder the terms:
4 + 4x + x2 = 48 + 4

Combine like terms: 48 + 4 = 52
4 + 4x + x2 = 52

Factor a perfect square on the left side:
(x + 2)(x + 2) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(x + 2) equal to 7.211102551 and -7.211102551.

Subproblem 1

x + 2 = 7.211102551 Simplifying x + 2 = 7.211102551 Reorder the terms: 2 + x = 7.211102551 Solving 2 + x = 7.211102551 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 = 7.211102551 + -2 Combine like terms: 2 + -2 = 0 0 + x = 7.211102551 + -2 x = 7.211102551 + -2 Combine like terms: 7.211102551 + -2 = 5.211102551 x = 5.211102551 Simplifying x = 5.211102551

Subproblem 2

x + 2 = -7.211102551 Simplifying x + 2 = -7.211102551 Reorder the terms: 2 + x = -7.211102551 Solving 2 + x = -7.211102551 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 = -7.211102551 + -2 Combine like terms: 2 + -2 = 0 0 + x = -7.211102551 + -2 x = -7.211102551 + -2 Combine like terms: -7.211102551 + -2 = -9.211102551 x = -9.211102551 Simplifying x = -9.211102551

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.211102551, -9.211102551}

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