What number must you add to complete the square? x2+10x=8
a.10
b.15
c. 25
d. 5

C) 25

Take half of the x coefficient 10 to get 10/2 = 5, then square that result to get 5^2 = 25

This is what you add to both sides

Doing so will have x^2+10x+25 factor to (x+5)^2 on the left side, which completes the square. On the right side, the 8 turns into 33

The steps look like this

x^2+10x = 8

x^2+10x+25 = 8+25 ... adding 25 to both sides

(x+5)^2 = 33 ... factoring

From here you would apply the square root property and subtract 5 from both sides.

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.

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