SOLUTION: Solve 6x^2+38x+12=0

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Question 194983: Solve 6x^2+38x+12=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

6x%5E2%2B38x%2B12=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=6, b=38, and c=12


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-%2838%29+%2B-+sqrt%28+%2838%29%5E2-4%286%29%2812%29+%29%29%2F%282%286%29%29 Plug in a=6, b=38, and c=12


x+=+%28-38+%2B-+sqrt%28+1444-4%286%29%2812%29+%29%29%2F%282%286%29%29 Square 38 to get 1444.


x+=+%28-38+%2B-+sqrt%28+1444-288+%29%29%2F%282%286%29%29 Multiply 4%286%29%2812%29 to get 288


x+=+%28-38+%2B-+sqrt%28+1156+%29%29%2F%282%286%29%29 Subtract 288 from 1444 to get 1156


x+=+%28-38+%2B-+sqrt%28+1156+%29%29%2F%2812%29 Multiply 2 and 6 to get 12.


x+=+%28-38+%2B-+34%29%2F%2812%29 Take the square root of 1156 to get 34.


x+=+%28-38+%2B+34%29%2F%2812%29 or x+=+%28-38+-+34%29%2F%2812%29 Break up the expression.


x+=+%28-4%29%2F%2812%29 or x+=++%28-72%29%2F%2812%29 Combine like terms.


x+=+-1%2F3 or x+=+-6 Simplify.


So the answers are x+=+-1%2F3 or x+=+-6