SOLUTION: 2x^2+5x-1 Find the x-intercepts for the function. x^2+5/2x=1/2 is where I am at now. I don't know how to get the next step to get the answer.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 2x^2+5x-1 Find the x-intercepts for the function. x^2+5/2x=1/2 is where I am at now. I don't know how to get the next step to get the answer.      Log On


   

Question 526361: 2x^2+5x-1
Find the x-intercepts for the function.
x^2+5/2x=1/2 is where I am at now. I don't know how to get the next step to get the answer.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the x-intercepts of 2x%5E2%2B5x-1, we need to solve 2x%5E2%2B5x-1=0 for x.




2x%5E2%2B5x-1=0 Start with the given equation.


Notice that the quadratic 2x%5E2%2B5x-1 is in the form of Ax%5E2%2BBx%2BC where A=2, B=5, and C=-1


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-%285%29+%2B-+sqrt%28+%285%29%5E2-4%282%29%28-1%29+%29%29%2F%282%282%29%29 Plug in A=2, B=5, and C=-1


x+=+%28-5+%2B-+sqrt%28+25-4%282%29%28-1%29+%29%29%2F%282%282%29%29 Square 5 to get 25.


x+=+%28-5+%2B-+sqrt%28+25--8+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-1%29 to get -8


x+=+%28-5+%2B-+sqrt%28+25%2B8+%29%29%2F%282%282%29%29 Rewrite sqrt%2825--8%29 as sqrt%2825%2B8%29


x+=+%28-5+%2B-+sqrt%28+33+%29%29%2F%282%282%29%29 Add 25 to 8 to get 33


x+=+%28-5+%2B-+sqrt%28+33+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%28-5%2Bsqrt%2833%29%29%2F%284%29 or x+=+%28-5-sqrt%2833%29%29%2F%284%29 Break up the expression.


So the exact solutions are x+=+%28-5%2Bsqrt%2833%29%29%2F%284%29 or x+=+%28-5-sqrt%2833%29%29%2F%284%29


which approximate to x+=+0.186 or x+=+-2.686 (by using a calculator)


So the x-intercepts are (0.186, 0) and (-2.686, 0)