Factoring A Quadratic that seems "unfactorable"! -16t^2+60t+5

Question

This quadratic seems impossible! We've tried almost every factor within 1-20 and none fit! How do I factor -16t^2+60t+5?! So aggravating!

 

We just need it FACTORED, not SOLVED.

Answer 1

-16t²+60t+5

(60-16t)t + 5

4(15-4t) + 5

245/4 - 16(t-15/8)²

245/4 - 1/4(8t-15)²

 

1/4 (-8t+7√5+15) (8t+7√5-15)

 

solution of roots below

 

-16t²+60t+5 = 0

÷ -16

 

t² - 15t/4 - 5/16 = 0

+ 5/16

 

t² - 15t/4 = 5/16

+ 225/64

 

t² - 15t/4 + 225/64 = 246/64

write left as a square

 

( t - 15/8)² = 245/64

√ of both sides

 

t - 15/8 = ±(7√5)/8

+ 15/8

 

t = 15/8±(7√5)/8

Answer 2

Hi Sam,

 

Soppose we set -16t^2+60t+5=0 and divide both sides by -16

 

gives t²-(15/4)t-5/16=0

  

t²-(15/4)t=5/16 add 5/16 to both sides

 

t²-(15/4)t+225/64=245/64 take 1/2 the coefficient of t, square it and add to both sides. This step is called completing the square because it makes the LHS a perfect square

 

(t-(15/8))² = 245/64 if you FOIL the LHS you will see that it checks

 

Now all you have to do is solve for t. It's not pretty but it works every time.

 

Jim