SOLUTION: How to solve 42 = -21t + 4.9t^2

Question 215011: How to solve 42 = -21t + 4.9t^2
Found 3 solutions by jim_thompson5910, stanbon, drj:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Multiply EVERY term by 10 to make every value a whole number.

Subtract 420 from both sides.

Rearrange the terms.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "t":

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

or Break up the expression.

So the solutions are or

which approximate to or

I'm assuming that the variable 't' is time. If so, then just ignore the second solution (as a negative time doesn't make sense).

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
solve 42 = -21t + 4.9t^2
4.9t^2 - 21t - 42 = 0
---
Use the Quadratic Formula:
t = [21 +- sqrt(21^2 - 4*4.9*-42)]/9.8
---
t = [21 +- sqrt(1264)]/9.8
--
t = [21 +- 35.56]/9.8
---
t = [21+35.56]/9.8 or t = [21-35.56]/9.8
--
t = 0.5771... or -1.486..
============================
Cheers,
Stan H.
Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!
How to solve 42 = -21t + 4.9t^2

Step 1. Subtract 42 from both sides of the equation and rearrange right side

Step 2. We can use the quadratic formula given as

where a =4.9, b=-21, and c=-42

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1264.2 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 5.77097859977151, -1.48526431405723. Here's your graph:

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J
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