SOLUTION: I am totally stuck. I do not think I can answer in decimals, yet that is what I keep coming up with. In other exercises like this I get an answer with a square root in it......

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I am totally stuck. I do not think I can answer in decimals, yet that is what I keep coming up with. In other exercises like this I get an answer with a square root in it......       Log On


   

Question 178424: I am totally stuck. I do not think I can answer in decimals, yet that is what I keep coming up with. In other exercises like this I get an answer with a square root in it......
solve 3x^2-5x-11=0
A. what are the solutions
B. What are the x intercepts
Simplify your answers. Type exact answers using radicals as needed. Express complex numbers in terms of i. Use commas to separate your answers as needed.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)

3x%5E2-5x-11=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=3, b=-5, and c=-11


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-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%283%29%28-11%29+%29%29%2F%282%283%29%29 Plug in a=3, b=-5, and c=-11


x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%283%29%28-11%29+%29%29%2F%282%283%29%29 Negate -5 to get 5.


x+=+%285+%2B-+sqrt%28+25-4%283%29%28-11%29+%29%29%2F%282%283%29%29 Square -5 to get 25.


x+=+%285+%2B-+sqrt%28+25--132+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-11%29 to get -132


x+=+%285+%2B-+sqrt%28+25%2B132+%29%29%2F%282%283%29%29 Rewrite sqrt%2825--132%29 as sqrt%2825%2B132%29


x+=+%285+%2B-+sqrt%28+157+%29%29%2F%282%283%29%29 Add 25 to 132 to get 157


x+=+%285+%2B-+sqrt%28+157+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%285%2Bsqrt%28157%29%29%2F%286%29 or x+=+%285-sqrt%28157%29%29%2F%286%29 Break up the expression.


So the answers are x+=+%285%2Bsqrt%28157%29%29%2F%286%29 or x+=+%285-sqrt%28157%29%29%2F%286%29


which approximate to x=2.922 or x=-1.255





b)

Since the solutions are approximately x=2.922 or x=-1.255, this means that the x-intercepts are approximately (2.922,0) and (-1.255,0)


Note: the solutions of any quadratic are the x-intercepts of the parabola