How to solve the quadratic equation -16t^2+65t+10 for zeros

Answer 1

-16t²+65t+10 = 0 (The "0" is required to make it an equation)

This is called the "standard form" for a quadratic....

How to solve:

This one is messy so it's good to look at the discriminator to verify that there are real solutions.

b² - 4ac = 652 -4*(-1)*10. This is positive, so there will be real solutions.

Make a list of the possible factors of -16, and of +10

Then, it's about "educated trial and error". To get that difference for the center term we need some large numbers.

For example, try (16x + 2) * ( -x + 5)

This gives us -16x² +78x +10 no good

If you can't find a combination that works, then you have to use the quadratic formula

Answer 2

-16t^2 + 65t + 10 = 0

16t^2 - 65t - 10 = 0

[65 +or- sqrt ( 65^2 + 4 *16*10)]/32

[ 65 +or- sqrt ( 4225 + 640)]/32 =

[ 65 +or- sqrt( 4865)]/32 =

[ 65 +or- sqrt( 4865)]/32 =

[ 65 + 69.749551969887233104330342293002....]/32

4.210923499.....