Question 907730
THE REASONING:
A) {{{system(height = -16t^2 + 32t +48, height=64)}}}--->{{{64= -16t^2 + 32t +48}}}
You solved that equation correctly and found {{{t=1}}} .
B) {{{system(height = -16t^2 + 32t +48, height=0)}}}--->{{{0= -16t^2 + 32t +48}}}
You solved that equation correctly and found {{{t=3}}} .
C) {{{system(height = -16t^2 + 32t +48, t=1/2)}}}--->{{{height = -16(1/2)^2 + 32(1/2) +48=-16(1/4)+16+48=-4+16-48=60}}} ,
and you did the calculation correctly.
 
THE QUADRATIC EQUATIONS:
There are many ways to solve. This is my way.
{{{64= -16t^2 + 32t +48}}}
{{{64-48= -16t^2 + 32t}}}
{{{16= -16t^2 + 32t}}}
(Here I would say that I am dividing both sides of the equal sign by -16, 
but I think of it as two steps)
Dividing both sides of the equation by 16, we get
{{{1=-t^2+2}}} , and changing the signs (multiplying both sides times -1), we get
{{{t^2-2t=-1}}}
Adding 1 to both sides, I complete the square:
{{{t^2-2t+1=-1+1}}}
{{{(t-1)^2=0}}}--->{{{t-1=0}}}--->{{{t=1}}}
 
{{{0= -16t^2 + 32t +48}}}
Dividing both sides by -16, I would get
{{{t^2-2t-3=0}}}
{{{t^2-2t=3}}}
{{{t^2-2t+1=3+1}}}
{{{(t-1)^2=4}}}--->{{{t-1=2}}}--->{{{t=3}}}