SOLUTION: How do you solve quadratic equations. example- -2d squared - 5d+19=0

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Question 176448This question is from textbook
: How do you solve quadratic equations. example- -2d squared - 5d+19=0 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
-2d%5E2-5d%2B19=0 Start with the given equation.


Notice we have a quadratic equation in the form of ad%5E2%2Bbd%2Bc where a=-2, b=-5, and c=19


Let's use the quadratic formula to solve for d


d+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


d+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%28-2%29%2819%29+%29%29%2F%282%28-2%29%29 Plug in a=-2, b=-5, and c=19


d+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%28-2%29%2819%29+%29%29%2F%282%28-2%29%29 Negate -5 to get 5.


d+=+%285+%2B-+sqrt%28+25-4%28-2%29%2819%29+%29%29%2F%282%28-2%29%29 Square -5 to get 25.


d+=+%285+%2B-+sqrt%28+25--152+%29%29%2F%282%28-2%29%29 Multiply 4%28-2%29%2819%29 to get -152


d+=+%285+%2B-+sqrt%28+25%2B152+%29%29%2F%282%28-2%29%29 Rewrite sqrt%2825--152%29 as sqrt%2825%2B152%29


d+=+%285+%2B-+sqrt%28+177+%29%29%2F%282%28-2%29%29 Add 25 to 152 to get 177


d+=+%285+%2B-+sqrt%28+177+%29%29%2F%28-4%29 Multiply 2 and -2 to get -4.


d+=+%285%2Bsqrt%28177%29%29%2F%28-4%29 or d+=+%285-sqrt%28177%29%29%2F%28-4%29 Break up the expression.


d+=+%28-5-sqrt%28177%29%29%2F%284%29 or d+=+%28-5%2Bsqrt%28177%29%29%2F%284%29 Reduce


So the answers are d+=+%28-5-sqrt%28177%29%29%2F%284%29 or d+=+%28-5%2Bsqrt%28177%29%29%2F%284%29


which approximate to d=-4.576 or d=2.076