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

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Question 215011: How to solve 42 = -21t + 4.9t^2
Found 3 solutions by jim_thompson5910, stanbon, drj:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
42+=+-21t+%2B+4.9t%5E2 Start with the given equation.


420+=+-210t+%2B+49t%5E2 Multiply EVERY term by 10 to make every value a whole number.


0+=+-210t+%2B+49t%5E2-420 Subtract 420 from both sides.


0+=+49t%5E2-210t-420 Rearrange the terms.


Notice that the quadratic 49t%5E2-210t-420 is in the form of At%5E2%2BBt%2BC where A=49, B=-210, and C=-420


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


t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


t+=+%28-%28-210%29+%2B-+sqrt%28+%28-210%29%5E2-4%2849%29%28-420%29+%29%29%2F%282%2849%29%29 Plug in A=49, B=-210, and C=-420


t+=+%28210+%2B-+sqrt%28+%28-210%29%5E2-4%2849%29%28-420%29+%29%29%2F%282%2849%29%29 Negate -210 to get 210.


t+=+%28210+%2B-+sqrt%28+44100-4%2849%29%28-420%29+%29%29%2F%282%2849%29%29 Square -210 to get 44100.


t+=+%28210+%2B-+sqrt%28+44100--82320+%29%29%2F%282%2849%29%29 Multiply 4%2849%29%28-420%29 to get -82320


t+=+%28210+%2B-+sqrt%28+44100%2B82320+%29%29%2F%282%2849%29%29 Rewrite sqrt%2844100--82320%29 as sqrt%2844100%2B82320%29


t+=+%28210+%2B-+sqrt%28+126420+%29%29%2F%282%2849%29%29 Add 44100 to 82320 to get 126420


t+=+%28210+%2B-+sqrt%28+126420+%29%29%2F%2898%29 Multiply 2 and 49 to get 98.


t+=+%28210+%2B-+14%2Asqrt%28645%29%29%2F%2898%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


t+=+%28210%2B14%2Asqrt%28645%29%29%2F%2898%29 or t+=+%28210-14%2Asqrt%28645%29%29%2F%2898%29 Break up the expression.


So the solutions are t+=+%28210%2B14%2Asqrt%28645%29%29%2F%2898%29 or t+=+%28210-14%2Asqrt%28645%29%29%2F%2898%29


which approximate to t=5.771 or t=-1.485


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) About Me  (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) About Me  (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

42-42+=+-21t+%2B+4.9t%5E2-42

0=+4.9t%5E2-21t-42

4.9t%5E2-21t-42=0

Step 2. We can use the quadratic formula given as

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

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

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case 4.9t%5E2%2B-21t%2B-42+=+0) has the following solutons:

t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-21%29%5E2-4%2A4.9%2A-42=1264.2.

Discriminant d=1264.2 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--21%2B-sqrt%28+1264.2+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%28-21%29%2Bsqrt%28+1264.2+%29%29%2F2%5C4.9+=+5.77097859977151
t%5B2%5D+=+%28-%28-21%29-sqrt%28+1264.2+%29%29%2F2%5C4.9+=+-1.48526431405723

Quadratic expression 4.9t%5E2%2B-21t%2B-42 can be factored:
4.9t%5E2%2B-21t%2B-42+=+4.9%28t-5.77097859977151%29%2A%28t--1.48526431405723%29
Again, the answer is: 5.77097859977151, -1.48526431405723. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4.9%2Ax%5E2%2B-21%2Ax%2B-42+%29



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