SOLUTION: 4x² + 19x + 21 = 0 x= ? x= ?

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Question 219573: 4x² + 19x + 21 = 0
x= ?
x= ?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2%2B19x%2B21=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=4, b=19, and c=21


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%284%29%2821%29+%29%29%2F%282%284%29%29 Plug in a=4, b=19, and c=21


x+=+%28-19+%2B-+sqrt%28+361-4%284%29%2821%29+%29%29%2F%282%284%29%29 Square 19 to get 361.


x+=+%28-19+%2B-+sqrt%28+361-336+%29%29%2F%282%284%29%29 Multiply 4%284%29%2821%29 to get 336


x+=+%28-19+%2B-+sqrt%28+25+%29%29%2F%282%284%29%29 Subtract 336 from 361 to get 25


x+=+%28-19+%2B-+sqrt%28+25+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%28-19+%2B-+5%29%2F%288%29 Take the square root of 25 to get 5.


x+=+%28-19+%2B+5%29%2F%288%29 or x+=+%28-19+-+5%29%2F%288%29 Break up the expression.


x+=+%28-14%29%2F%288%29 or x+=++%28-24%29%2F%288%29 Combine like terms.


x+=+-7%2F4 or x+=+-3 Simplify.


So the answers are x+=+-7%2F4 or x+=+-3