x^2+4=4+2(x+2)

Solution for x^2+4=4+2(x+2) equation:

x^2+4=4+2(x+2)

We move all terms to the left:

x^2+4-(4+2(x+2))=0


We calculate terms in parentheses: -(4+2(x+2)), so:

4+2(x+2)

determiningTheFunctionDomain
2(x+2)+4

We multiply parentheses

2x+4+4

We add all the numbers together, and all the variables

2x+8

Back to the equation:

-(2x+8)


We get rid of parentheses

x^2-2x-8+4=0

We add all the numbers together, and all the variables

x^2-2x-4=0

a = 1; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·1·(-4)
Δ = 20
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{5}}{2*1}=\frac{2-2\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{5}}{2*1}=\frac{2+2\sqrt{5}}{2}
$