SOLUTION: I don't understand this particular question. It says to solve by the method that's easiest to me, but all the methods are difficult for me. The problem is 3x^2=2x+5.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I don't understand this particular question. It says to solve by the method that's easiest to me, but all the methods are difficult for me. The problem is 3x^2=2x+5.      Log On


   

Question 147538This question is from textbook algebra
: I don't understand this particular question. It says to solve by the method that's easiest to me, but all the methods are difficult for me. The problem is 3x^2=2x+5. This question is from textbook algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2=2x%2B5 Start with the given equation.


3x%5E2-2x-5=0 Subtract 2x from both sides. Subtract 5 from both sides.


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


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


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


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


x+=+%282+%2B-+sqrt%28+4--60+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-5%29 to get -60


x+=+%282+%2B-+sqrt%28+4%2B60+%29%29%2F%282%283%29%29 Rewrite sqrt%284--60%29 as sqrt%284%2B60%29


x+=+%282+%2B-+sqrt%28+64+%29%29%2F%282%283%29%29 Add 4 to 60 to get 64


x+=+%282+%2B-+sqrt%28+64+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%282+%2B-+8%29%2F%286%29 Take the square root of 64 to get 8.


x+=+%282+%2B+8%29%2F%286%29 or x+=+%282+-+8%29%2F%286%29 Break up the expression.


x+=+%2810%29%2F%286%29 or x+=++%28-6%29%2F%286%29 Combine like terms.


x+=+5%2F3 or x+=+-1 Simplify.


So our answers are x+=+5%2F3 or x+=+-1