Answer:
[tex]x=4[/tex] or [tex]x=-1.33[/tex]
Step-by-step explanation:
From the triangle shown,
EG = DG
Plug in [tex]3x^{2} -8x[/tex] for EG and 16 for DG. Solve for x.
[tex]3x^{2} -8x=16\\3x^{2} -8x-16=0[/tex]
The above equation is a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] with a = 3, b = -8 and c = -16.
Now, using the quadratic formula, we solve for x.
[tex]x=\frac{-b}{2a}[/tex] ± [tex]\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]
Plug in 3 for a, -8 for b and -16 for c.
[tex]x=\frac{-(-8)}{2(3)}[/tex] ± [tex]\frac{\sqrt{(-8)^{2}-4(3)(-16) } }{2(3)}[/tex]
[tex]x=\frac{4}{3}[/tex] ± [tex]\frac{\sqrt{256} }{6}[/tex]
[tex]x=\frac{4}{3}[/tex] ± [tex]\frac{8}{3}[/tex]
[tex]x=\frac{4}{3}+\frac{8}{3}=4[/tex] or
[tex]x=\frac{4}{3}-\frac{8}{3}=-1.33[/tex]
Therefore, possible values of [tex]x[/tex] are -1.33 or 4.
