Question

Will someone help me with this please!!! I don’t know how to find the answer!

Answer 1

Answer:

$x=4$ or $x=-1.33$

Step-by-step explanation:

From the triangle shown,

EG = DG

Plug in $3x^{2} -8x$ for EG and 16 for DG. Solve for x.

$3x^{2} -8x=16\\3x^{2} -8x-16=0$

The above equation is a quadratic equation of the form $ax^{2} +bx+c=0$ with a = 3, b = -8 and c = -16.

Now, using the quadratic formula, we solve for x.

$x=\frac{-b}{2a}$ ± $\frac{\sqrt{b^{2}-4ac } }{2a}$

Plug in 3 for a, -8 for b and -16 for c.

$x=\frac{-(-8)}{2(3)}$ ± $\frac{\sqrt{(-8)^{2}-4(3)(-16) } }{2(3)}$

$x=\frac{4}{3}$ ± $\frac{\sqrt{256} }{6}$

$x=\frac{4}{3}$ ± $\frac{8}{3}$

$x=\frac{4}{3}+\frac{8}{3}=4$ or

$x=\frac{4}{3}-\frac{8}{3}=-1.33$

Therefore, possible values of $x$ are -1.33 or 4.