SOLUTION: Solve. {{{ 6x^2 + 13x + 6 = 0 }}}

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Question 308973: Solve.
+6x%5E2+%2B+13x+%2B+6+=+0+
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

6x%5E2%2B13x%2B6=0 Start with the given equation.


Notice that the quadratic 6x%5E2%2B13x%2B6 is in the form of Ax%5E2%2BBx%2BC where A=6, B=13, and C=6


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-%2813%29+%2B-+sqrt%28+%2813%29%5E2-4%286%29%286%29+%29%29%2F%282%286%29%29 Plug in A=6, B=13, and C=6


x+=+%28-13+%2B-+sqrt%28+169-4%286%29%286%29+%29%29%2F%282%286%29%29 Square 13 to get 169.


x+=+%28-13+%2B-+sqrt%28+169-144+%29%29%2F%282%286%29%29 Multiply 4%286%29%286%29 to get 144


x+=+%28-13+%2B-+sqrt%28+25+%29%29%2F%282%286%29%29 Subtract 144 from 169 to get 25


x+=+%28-13+%2B-+sqrt%28+25+%29%29%2F%2812%29 Multiply 2 and 6 to get 12.


x+=+%28-13+%2B-+5%29%2F%2812%29 Take the square root of 25 to get 5.


x+=+%28-13+%2B+5%29%2F%2812%29 or x+=+%28-13+-+5%29%2F%2812%29 Break up the expression.


x+=+%28-8%29%2F%2812%29 or x+=++%28-18%29%2F%2812%29 Combine like terms.


x+=+-2%2F3 or x+=+-3%2F2 Simplify.


So the solutions are x+=+-2%2F3 or x+=+-3%2F2