The quadratic formula is:
x=(-b+-sqrt(b^2-4ac))/(2a)x=−b±√b2−4ac2a
where ax^2+bx+c=0ax2+bx+c=0
Here is your quadratic equation
h=-16t^2+50t+4h=−16t2+50t+4
Looking at ax^2+bx+c=0ax2+bx+c=0
I can see that your values are...
a=-16a=−16
b=50b=50
c=4c=4
Now just put those values into the quadratic formula
h=(-b+-sqrt(b^2-4ac))/(2a)h=−b±√b2−4ac2a
h=(-(50)+-sqrt((50)^2-4(-16)(4)))/(2(-16))h=−(50)±√(50)2−4(−16)(4)2(−16)
h=(-50+-sqrt(2500+256))/(-32)h=−50±√2500+256−32
Negative divided by negative makes our numerator and denominator positive
h=(50+-sqrt(2756))/(32)h=50±√275632
You might think we are finished here but remember to always check if you can simplify the square root. In this case 27562756 can be divided by 44, which will give us a 22 outside of the square root.
h=(50+-sqrt(4*689))/(32)h=50±√4⋅68932
h=(50+-2sqrt(689))/(32)h=50±2√68932
Now notice how we can factor 22 out of our problem, thanks to simplifying the square root
h=[2(25+-sqrt(689))]/[2(16)]h=2(25±√689)2(16)
Cancel the common factors
h=[cancel2(25+-sqrt(689))]/[cancel2(16)]
h=(25+-sqrt(689))/(16)
So our answers are...
color(green)[h=(25+sqrt(689))/(16)]
color(green)[h=(25-sqrt(689))/(16)]
