Solve. V^2-6v-16=0
Factorize expression:
V^2-6v-16=0
(V-8)(V+2)=0
Solve for (V-8)=0 or (V+2)=0 to get
V=8 or V=-2.
To solve the quadratic equation v^2 - 6v - 16 = 0, we can use the quadratic formula:
v = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 1, b = -6, and c = -16.
Substituting these values into the quadratic formula, we get:
v = (-(-6) ± √((-6)^2 - 4 * 1 * -16)) / (2 * 1)
Simplifying further:
v = (6 ± √(36 + 64)) / 2
v = (6 ± √100) / 2
v = (6 ± 10) / 2
Now, let's solve for the two possible values of v:
1) When v = (6 + 10) / 2:
v = 16 / 2
v = 8
2) When v = (6 - 10) / 2:
v = -4 / 2
v = -2
Therefore, the solutions to the quadratic equation v^2 - 6v - 16 = 0 are v = 8 and v = -2.