Question

Solve for x in the equation x2 + 14x+17--96

x=-7+4/6;

x=-7 + 8i

x=7+4/6;

x = 7 + 8i

Answer 1

Answer:

Option B.

Step-by-step explanation:

If a quadratic equation is defined as $ax^2+bx+c=0$, the by quadratic formula

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

Consider the given equation is

$x^2+14x+17=-96$

We need to find the value of x.

Add 96 on both sides.

$x^2+14x+17+96=-96+96$

$x^2+14x+113=0$

Here, a=1, b=14 and c=113. Using quadratic formula we get

$x=\dfrac{-14\pm \sqrt{14^2-4(1)(113)}}{2(1)}$

$x=\dfrac{-14\pm \sqrt{-256}}{2(1)}$

$x=\dfrac{-14\pm \sqrt{256}\sqrt{-1}}{2}$           $(\sqrt{-1}=i)$

$x=\dfrac{-14\pm 16i}{2}$

$x=-7\pm 8i$

The value of x are x=-7 + 8i and x=-7 - 8i.

Therefore, the correct option is B.