Answer:
-4 ± 2√6
Step-by-step explanation:
Rewritten in standard quadratic form, x^2+8x-2=18 becomes x^2 + 8x - 20 = 0.
Here the quadratic coefficients are a = 1, b = 8 and c = -20 and so the discriminant is b^2 - 4ac, or 8^2 - 4(1)(-20), or 96.
Because the discriminant is positive, we know that this quadratic has two different real roots. These roots are:
-b ± √(b² - 4ac)
x = -------------------------
2a
which in this case comes out to:
-8 ± √96 -8 ± 4√6
x = ------------------ = ------------------- = -4 ± 2√6
2 2
From the picture you can see that TY bisects angle T.
Use the bisector property:
.
If YK=68 mm and VK=x mm, then VY=x-68 mm.
Then
.
Express x-68:
mm.
Therefore, x=30+68=98 mm.
Answer: x=98 mm.