SOLUTION: Please help me solve the quadratic equation 3x^2+19x-14=0 using the quadratic formula.

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Question 632702: Please help me solve the quadratic equation 3x^2+19x-14=0 using the quadratic formula.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2%2B19x-14=0 Start with the given equation.


Notice that the quadratic 3x%5E2%2B19x-14 is in the form of Ax%5E2%2BBx%2BC where A=3, B=19, and C=-14


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-%2819%29+%2B-+sqrt%28+%2819%29%5E2-4%283%29%28-14%29+%29%29%2F%282%283%29%29 Plug in A=3, B=19, and C=-14


x+=+%28-19+%2B-+sqrt%28+361-4%283%29%28-14%29+%29%29%2F%282%283%29%29 Square 19 to get 361.


x+=+%28-19+%2B-+sqrt%28+361--168+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-14%29 to get -168


x+=+%28-19+%2B-+sqrt%28+361%2B168+%29%29%2F%282%283%29%29 Rewrite sqrt%28361--168%29 as sqrt%28361%2B168%29


x+=+%28-19+%2B-+sqrt%28+529+%29%29%2F%282%283%29%29 Add 361 to 168 to get 529


x+=+%28-19+%2B-+sqrt%28+529+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%28-19+%2B-+23%29%2F%286%29 Take the square root of 529 to get 23.


x+=+%28-19+%2B+23%29%2F%286%29 or x+=+%28-19+-+23%29%2F%286%29 Break up the expression.


x+=+%284%29%2F%286%29 or x+=++%28-42%29%2F%286%29 Combine like terms.


x+=+2%2F3 or x+=+-7 Simplify.


So the solutions are x+=+2%2F3 or x+=+-7

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