SOLUTION: can you please help me solve by using the quadratic formula and leave irrational roots in the simplest radical form {{{ 3x^2-4x-5=0 }}}

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Question 197972This question is from textbook algebra sturcture and method
: can you please help me solve by using the quadratic formula and leave irrational roots in the simplest radical form +3x%5E2-4x-5=0+ This question is from textbook algebra sturcture and method

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

3x%5E2-4x-5=0 Start with the given equation.


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


x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%283%29%28-5%29+%29%29%2F%282%283%29%29 Negate -4 to get 4.


x+=+%284+%2B-+sqrt%28+16-4%283%29%28-5%29+%29%29%2F%282%283%29%29 Square -4 to get 16.


x+=+%284+%2B-+sqrt%28+16--60+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-5%29 to get -60


x+=+%284+%2B-+sqrt%28+16%2B60+%29%29%2F%282%283%29%29 Rewrite sqrt%2816--60%29 as sqrt%2816%2B60%29


x+=+%284+%2B-+sqrt%28+76+%29%29%2F%282%283%29%29 Add 16 to 60 to get 76


x+=+%284+%2B-+sqrt%28+76+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%284+%2B-+2%2Asqrt%2819%29%29%2F%286%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%284%2B2%2Asqrt%2819%29%29%2F%286%29 or x+=+%284-2%2Asqrt%2819%29%29%2F%286%29 Break up the expression.


x+=+%282%2Bsqrt%2819%29%29%2F%283%29 or x+=+%282-sqrt%2819%29%29%2F%283%29 Reduce.


So the solutions are x+=+%282%2Bsqrt%2819%29%29%2F%283%29 or x+=+%282-sqrt%2819%29%29%2F%283%29