SOLUTION: solve : {{{ 3x^2+ 8x-24=0 }}}

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Question 592841: solve : +3x%5E2%2B+8x-24=0+
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2%2B8x-24=0 Start with the given equation.


Notice that the quadratic 3x%5E2%2B8x-24 is in the form of Ax%5E2%2BBx%2BC where A=3, B=8, and C=-24


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%28-24%29+%29%29%2F%282%283%29%29 Plug in A=3, B=8, and C=-24


x+=+%28-8+%2B-+sqrt%28+64-4%283%29%28-24%29+%29%29%2F%282%283%29%29 Square 8 to get 64.


x+=+%28-8+%2B-+sqrt%28+64--288+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-24%29 to get -288


x+=+%28-8+%2B-+sqrt%28+64%2B288+%29%29%2F%282%283%29%29 Rewrite sqrt%2864--288%29 as sqrt%2864%2B288%29


x+=+%28-8+%2B-+sqrt%28+352+%29%29%2F%282%283%29%29 Add 64 to 288 to get 352


x+=+%28-8+%2B-+sqrt%28+352+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%28-8+%2B-+4%2Asqrt%2822%29%29%2F%286%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-8%2B4%2Asqrt%2822%29%29%2F%286%29 or x+=+%28-8-4%2Asqrt%2822%29%29%2F%286%29 Break up the expression.


x+=+%28-4%2B2%2Asqrt%2822%29%29%2F%283%29 or x+=+%28-4-2%2Asqrt%2822%29%29%2F%283%29 Reduce


So the solutions are x+=+%28-4%2B2%2Asqrt%2822%29%29%2F%283%29 or x+=+%28-4-2%2Asqrt%2822%29%29%2F%283%29