(x+2)*(x+2)=x*2+6

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Solution for (x+2)*(x+2)=x*2+6 equation:


Simplifying
(x + 2)(x + 2) = x * 2 + 6

Reorder the terms:
(2 + x)(x + 2) = x * 2 + 6

Reorder the terms:
(2 + x)(2 + x) = x * 2 + 6

Multiply (2 + x) * (2 + x)
(2(2 + x) + x(2 + x)) = x * 2 + 6
((2 * 2 + x * 2) + x(2 + x)) = x * 2 + 6
((4 + 2x) + x(2 + x)) = x * 2 + 6
(4 + 2x + (2 * x + x * x)) = x * 2 + 6
(4 + 2x + (2x + x2)) = x * 2 + 6

Combine like terms: 2x + 2x = 4x
(4 + 4x + x2) = x * 2 + 6

Reorder the terms for easier multiplication:
4 + 4x + x2 = 2x + 6

Reorder the terms:
4 + 4x + x2 = 6 + 2x

Solving
4 + 4x + x2 = 6 + 2x

Solving for variable 'x'.

Reorder the terms:
4 + -6 + 4x + -2x + x2 = 6 + 2x + -6 + -2x

Combine like terms: 4 + -6 = -2
-2 + 4x + -2x + x2 = 6 + 2x + -6 + -2x

Combine like terms: 4x + -2x = 2x
-2 + 2x + x2 = 6 + 2x + -6 + -2x

Reorder the terms:
-2 + 2x + x2 = 6 + -6 + 2x + -2x

Combine like terms: 6 + -6 = 0
-2 + 2x + x2 = 0 + 2x + -2x
-2 + 2x + x2 = 2x + -2x

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 2 + 1

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

Combine like terms: 2 + 1 = 3
1 + 2x + x2 = 3

Factor a perfect square on the left side:
(x + 1)(x + 1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + 1) equal to 1.732050808 and -1.732050808.

Subproblem 1

x + 1 = 1.732050808 Simplifying x + 1 = 1.732050808 Reorder the terms: 1 + x = 1.732050808 Solving 1 + x = 1.732050808 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 = 1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.732050808 + -1 x = 1.732050808 + -1 Combine like terms: 1.732050808 + -1 = 0.732050808 x = 0.732050808 Simplifying x = 0.732050808

Subproblem 2

x + 1 = -1.732050808 Simplifying x + 1 = -1.732050808 Reorder the terms: 1 + x = -1.732050808 Solving 1 + x = -1.732050808 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 = -1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.732050808 + -1 x = -1.732050808 + -1 Combine like terms: -1.732050808 + -1 = -2.732050808 x = -2.732050808 Simplifying x = -2.732050808

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.732050808, -2.732050808}

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