SOLUTION: 3x^2 + 8x - 3 = 0

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Question 151294: 3x^2 + 8x - 3 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2%2B8x-3=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=3, b=8, and c=-3


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-%288%29+%2B-+sqrt%28+%288%29%5E2-4%283%29%28-3%29+%29%29%2F%282%283%29%29 Plug in a=3, b=8, and c=-3


x+=+%28-8+%2B-+sqrt%28+64-4%283%29%28-3%29+%29%29%2F%282%283%29%29 Square 8 to get 64.


x+=+%28-8+%2B-+sqrt%28+64--36+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-3%29 to get -36


x+=+%28-8+%2B-+sqrt%28+64%2B36+%29%29%2F%282%283%29%29 Rewrite sqrt%2864--36%29 as sqrt%2864%2B36%29


x+=+%28-8+%2B-+sqrt%28+100+%29%29%2F%282%283%29%29 Add 64 to 36 to get 100


x+=+%28-8+%2B-+sqrt%28+100+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%28-8+%2B-+10%29%2F%286%29 Take the square root of 100 to get 10.


x+=+%28-8+%2B+10%29%2F%286%29 or x+=+%28-8+-+10%29%2F%286%29 Break up the expression.


x+=+%282%29%2F%286%29 or x+=++%28-18%29%2F%286%29 Combine like terms.


x+=+1%2F3 or x+=+-3 Simplify.


So our answers are x+=+1%2F3 or x+=+-3