SOLUTION: Solve 3x^2-7x-13=0

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Question 407835: Solve 3x^2-7x-13=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
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3x%5E2-7x-13=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=3, b=-7, and c=-13


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-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%283%29%28-13%29+%29%29%2F%282%283%29%29 Plug in a=3, b=-7, and c=-13


x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%283%29%28-13%29+%29%29%2F%282%283%29%29 Negate -7 to get 7.


x+=+%287+%2B-+sqrt%28+49-4%283%29%28-13%29+%29%29%2F%282%283%29%29 Square -7 to get 49.


x+=+%287+%2B-+sqrt%28+49--156+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-13%29 to get -156


x+=+%287+%2B-+sqrt%28+49%2B156+%29%29%2F%282%283%29%29 Rewrite sqrt%2849--156%29 as sqrt%2849%2B156%29


x+=+%287+%2B-+sqrt%28+205+%29%29%2F%282%283%29%29 Add 49 to 156 to get 205


x+=+%287+%2B-+sqrt%28+205+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%287%2Bsqrt%28205%29%29%2F%286%29 or x+=+%287-sqrt%28205%29%29%2F%286%29 Break up the expression.


So the answers are x+=+%287%2Bsqrt%28205%29%29%2F%286%29 or x+=+%287-sqrt%28205%29%29%2F%286%29


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