SOLUTION: Hi, Can someone please help me with the following: I have two equations that I need to solve using the quadratic equation but, I really having problems solving them. 1. 5/

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hi, Can someone please help me with the following: I have two equations that I need to solve using the quadratic equation but, I really having problems solving them. 1. 5/      Log On


   

Question 154336: Hi,
Can someone please help me with the following:
I have two equations that I need to solve using the quadratic equation but, I really having problems solving them.
1. 5/6x^2-7x-6/5=0

2. 3^1/2y^2-4y-7(3)^1/2=0
Thank you so much, I am sorry for being so much trouble but I been out of school for 15 years.
Jimmy
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started.

# 1


%285%2F6%29x%5E2-7x-6%2F5=0 Start with the given equation.


30%28%285%2Fcross%286%29%29x%5E2-7x-6%2Fcross%285%29%29=30%280%29 Multiply both sides by 30 to clear the fractions.


25x%5E2-210x-36=0 Distribute and multiply


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=25, b=-210, and c=-36


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-210%29+%2B-+sqrt%28+%28-210%29%5E2-4%2825%29%28-36%29+%29%29%2F%282%2825%29%29 Plug in a=25, b=-210, and c=-36


x+=+%28210+%2B-+sqrt%28+%28-210%29%5E2-4%2825%29%28-36%29+%29%29%2F%282%2825%29%29 Negate -210 to get 210.


x+=+%28210+%2B-+sqrt%28+44100-4%2825%29%28-36%29+%29%29%2F%282%2825%29%29 Square -210 to get 44100.


x+=+%28210+%2B-+sqrt%28+44100--3600+%29%29%2F%282%2825%29%29 Multiply 4%2825%29%28-36%29 to get -3600


x+=+%28210+%2B-+sqrt%28+44100%2B3600+%29%29%2F%282%2825%29%29 Rewrite sqrt%2844100--3600%29 as sqrt%2844100%2B3600%29


x+=+%28210+%2B-+sqrt%28+47700+%29%29%2F%282%2825%29%29 Add 44100 to 3600 to get 47700


x+=+%28210+%2B-+sqrt%28+47700+%29%29%2F%2850%29 Multiply 2 and 25 to get 50.


x+=+%28210+%2B-+30%2Asqrt%2853%29%29%2F%2850%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28210%2B30%2Asqrt%2853%29%29%2F%2850%29 or x+=+%28210-30%2Asqrt%2853%29%29%2F%2850%29 Break up the expression.


x+=+%2821%2B3%2Asqrt%2853%29%29%2F%285%29 or x+=+%2821-3%2Asqrt%2853%29%29%2F%285%29 Reduce

So the answers are x+=+%2821%2B3%2Asqrt%2853%29%29%2F%285%29 or x+=+%2821-3%2Asqrt%2853%29%29%2F%285%29


which approximate to x=8.568 or x=-0.168