2 questions?

Question

solve: 0=16t^2+8t+15

solve 4=16t^2+14t+4

Answer 1

1. First: factor: take the first coefficient and multiply it by the last coefficient (16*15 = 240). Find two numbers that give you 240 when multiplied; and 8 (middle coefficient) when added/subtracted. The numbers are: 12, 20

Second: rewrite the equation, group "like" terms and factor each set:

(16t^2 + 12t) + (20t + 15) = 0

4t(4t + 3) + 5(4t + 3) = 0

(4t + 3)(4t + 5) = 0

Third: solve for "t" variables > make each set equal zero:

4t + 3 = 0
4t + 3 - 3 = 0 - 3
4t = -3
4t/4 = -3/4 > t = -3/4

4t + 5 = 0
4t + 5 - 5 = 0 - 5
4t = -5
4t/4= -5/4 > t = -5/4

2. follow the same format.

Answer 2

Instead of giving you the answer, I will show you how to solve these.

The first step is to make the equation equal to 0. The first one already is. The second one is not. You get: 16t^2+14t+4 -4 =0

The next step is to simplify when posible. Here again, it only applies to the 2nd equation: 8t^2 + 7t = 0

At this point, the equation are in the standard format to solve using the quadratic equation ([-b +/- sqrt (b^2 -4ac)]/2a).
a is the coefficient of x^2
b is the coefficient of x
c is the term with no x. Note this is 0 when this term does not exist as in the simplified 2nd equation.

Answer 3

16t^2+ 8t + 15 = 0

t= [-8 +/- sqrt (8^2 - 4*16*15)]/2*16

No real roots

16t^2 + 14t +4 = 4

16t^2 + 14 t = 0

t(16t + 14) = 0

Roots: t= 0 and t = -14/16= - 7/8

If t = time, then t = 0 is the only root


Ana