SOLUTION: (a) 3x^2 - 10x - 8 = 0

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Question 167791: (a) 3x^2 - 10x - 8 = 0
Answer by jim_thompson5910(28598) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2-10x-8=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=3, b=-10, and c=-8


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-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2-4%283%29%28-8%29+%29%29%2F%282%283%29%29 Plug in a=3, b=-10, and c=-8


x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%283%29%28-8%29+%29%29%2F%282%283%29%29 Negate -10 to get 10.


x+=+%2810+%2B-+sqrt%28+100-4%283%29%28-8%29+%29%29%2F%282%283%29%29 Square -10 to get 100.


x+=+%2810+%2B-+sqrt%28+100--96+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-8%29 to get -96


x+=+%2810+%2B-+sqrt%28+100%2B96+%29%29%2F%282%283%29%29 Rewrite sqrt%28100--96%29 as sqrt%28100%2B96%29


x+=+%2810+%2B-+sqrt%28+196+%29%29%2F%282%283%29%29 Add 100 to 96 to get 196


x+=+%2810+%2B-+sqrt%28+196+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%2810+%2B-+14%29%2F%286%29 Take the square root of 196 to get 14.


x+=+%2810+%2B+14%29%2F%286%29 or x+=+%2810+-+14%29%2F%286%29 Break up the expression.


x+=+%2824%29%2F%286%29 or x+=++%28-4%29%2F%286%29 Combine like terms.


x+=+4 or x+=+-2%2F3 Simplify.


So the answers are x+=+4 or x+=+-2%2F3