SOLUTION: 3x^2-5x-8=0

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Question 540548: 3x^2-5x-8=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
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3x%5E2-5x-8=0 Start with the given equation.


Notice that the quadratic 3x%5E2-5x-8 is in the form of Ax%5E2%2BBx%2BC where A=3, B=-5, 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-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%283%29%28-8%29+%29%29%2F%282%283%29%29 Plug in A=3, B=-5, and C=-8


x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%283%29%28-8%29+%29%29%2F%282%283%29%29 Negate -5 to get 5.


x+=+%285+%2B-+sqrt%28+25-4%283%29%28-8%29+%29%29%2F%282%283%29%29 Square -5 to get 25.


x+=+%285+%2B-+sqrt%28+25--96+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-8%29 to get -96


x+=+%285+%2B-+sqrt%28+25%2B96+%29%29%2F%282%283%29%29 Rewrite sqrt%2825--96%29 as sqrt%2825%2B96%29


x+=+%285+%2B-+sqrt%28+121+%29%29%2F%282%283%29%29 Add 25 to 96 to get 121


x+=+%285+%2B-+sqrt%28+121+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%285+%2B-+11%29%2F%286%29 Take the square root of 121 to get 11.


x+=+%285+%2B+11%29%2F%286%29 or x+=+%285+-+11%29%2F%286%29 Break up the expression.


x+=+%2816%29%2F%286%29 or x+=++%28-6%29%2F%286%29 Combine like terms.


x+=+8%2F3 or x+=+-1 Simplify.


So the solutions are x+=+8%2F3 or x+=+-1


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