SOLUTION: how do you solve 6x^2-11x-35=0

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Question 555324: how do you solve 6x^2-11x-35=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

6x%5E2-11x-35=0 Start with the given equation.


Notice that the quadratic 6x%5E2-11x-35 is in the form of Ax%5E2%2BBx%2BC where A=6, B=-11, and C=-35


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-%28-11%29+%2B-+sqrt%28+%28-11%29%5E2-4%286%29%28-35%29+%29%29%2F%282%286%29%29 Plug in A=6, B=-11, and C=-35


x+=+%2811+%2B-+sqrt%28+%28-11%29%5E2-4%286%29%28-35%29+%29%29%2F%282%286%29%29 Negate -11 to get 11.


x+=+%2811+%2B-+sqrt%28+121-4%286%29%28-35%29+%29%29%2F%282%286%29%29 Square -11 to get 121.


x+=+%2811+%2B-+sqrt%28+121--840+%29%29%2F%282%286%29%29 Multiply 4%286%29%28-35%29 to get -840


x+=+%2811+%2B-+sqrt%28+121%2B840+%29%29%2F%282%286%29%29 Rewrite sqrt%28121--840%29 as sqrt%28121%2B840%29


x+=+%2811+%2B-+sqrt%28+961+%29%29%2F%282%286%29%29 Add 121 to 840 to get 961


x+=+%2811+%2B-+sqrt%28+961+%29%29%2F%2812%29 Multiply 2 and 6 to get 12.


x+=+%2811+%2B-+31%29%2F%2812%29 Take the square root of 961 to get 31.


x+=+%2811+%2B+31%29%2F%2812%29 or x+=+%2811+-+31%29%2F%2812%29 Break up the expression.


x+=+%2842%29%2F%2812%29 or x+=++%28-20%29%2F%2812%29 Combine like terms.


x+=+7%2F2 or x+=+-5%2F3 Simplify.


So the solutions are x+=+7%2F2 or x+=+-5%2F3

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