(X2+2)+y2=16

Solution for (X2+2)+y2=16 equation:

(X2+2)+X2=16

We move all terms to the left:

(X2+2)+X2-(16)=0

We add all the numbers together, and all the variables

(+X^2+2)+X2-16=0

We add all the numbers together, and all the variables

X^2+(+X^2+2)-16=0

We get rid of parentheses

X^2+X^2+2-16=0

We add all the numbers together, and all the variables

2X^2-14=0

a = 2; b = 0; c = -14;
Δ = b2-4ac
Δ = 02-4·2·(-14)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{7}}{2*2}=\frac{0-4\sqrt{7}}{4}
=-\frac{4\sqrt{7}}{4}
=-\sqrt{7}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{7}}{2*2}=\frac{0+4\sqrt{7}}{4}
=\frac{4\sqrt{7}}{4}
=\sqrt{7}
$