Solving a Quadratic Equation

[purp!chickpot822]

In the College Algebra Section for Graphing Functions, Question 26:

I really need help with the detail of solving this problem. Can someone please show me the step by step process in figuring out this problem? I have tried to calculate it many times and cannot for the life of me come up with the correct answer.

I am familiar with the quadratic formula but for some reason cannot get it to work for this problem, I am sure that I am missing a step.

“An object is thrown directly upward from a starting height of 25 ft and a starting velocity of 85 ft per second. The following function describes the height of the object with respect to the time, t.”

h(t) = -16t2 + 85t + 25

How long does it take before the object reaches the ground? Round you answer to the nearest hundredths place.

The answer is 5.59.

[jmeitrem]

h(t) = -16t2 + 85t + 25

a = -16
b = 85
c = 25

quadratic formula = [-b +- Sqrt(b^2 - 4ac)] / 2a

= [-85 +- Sqrt((85^2) - 4(-16)(25))] / 2(-16)

= [-85 +- Sqrt(8825)] / -32

[-85 + Sqrt(8825)] / -32 = a negative number
[-85 - Sqrt(8825)] / -32 = 5.59

[purp!chickpot822]

Thank you jmeitrem,

I know know the steps, and I know what numbers to plug in where they are supposed to be, however I cannot come up to 5.59. Even plugging this in to a scientific calculator does not yield 5.59.

In previous videos on solving using the quadratic formula, the instructions were as follows:

Solve 49x^2 + 80x + 20

-80 (plus/minus) sqrt(80^2 - 4(49)(20)/ 2(49)

ends up being sqrt (2480)

(2480) is then broken down into 10 times 248

10 is broken down into 2 times 5 and 248 is broken down into 2 times 124

124 is broken down into 2 times 62

62 is broken down into 2 times 31

then you factor out all 2's (there are two pair) and you are left with 5 and 31

this all equals -80 (plus/minus) 2 times 2 sqrt 155 (155 is the product of 5 and 31)

then you factor out all 2's

this leaves you with -40 (plus/minus) sqrt 155

It is all of this middle stuff that I am missing. Anyway, thank you for your help! I am going crazy!

[purp!chickpot822]

sorry,

the result of the example I mentioned is

-40-sqrt (155)/49

I forgot to list the denominator.

:-)

[jmeitrem]

Before plugging it into the calculator it's helpful to work out what's under the square root first. This helps to avoid any mistakes with negatives and parentheses. It's not going to come out pretty so there's not much point in breaking it down like in your example. It's just sqrt(8825)

This is what I plugged in to the calculator:
(-85 - Sqrt(8825)) / -32 = 5.591920973

[purp!chickpot822]

Before plugging it into the calculator it's helpful to work out what's under the square root first. This helps to avoid any mistakes with negatives and parentheses. It's not going to come out pretty so there's not much point in breaking it down like in your example. It's just sqrt(8825)

This is what I plugged in to the calculator:
(-85 - Sqrt(8825)) / -32 = 5.591920973

I cannot believe how stupid I was! I was forgetting to put in the extra right parentheses after 8825. Thank you for your explanation, now I am coming up with the correct answer.

Sometimes, studying for hours, makes me do the stupidest things! I knew I was forgetting something but just could not see it.

Thank you so much for taking the time to help me!