SOLUTION: Solve for x. 2x squared plus 6x=3

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Question 407319: Solve for x. 2x squared plus 6x=3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2%2B6x=3 Start with the given equation.


2x%5E2%2B6x-3=0 Subtract 3 from both sides.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=6, and c=-3


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-%286%29+%2B-+sqrt%28+%286%29%5E2-4%282%29%28-3%29+%29%29%2F%282%282%29%29 Plug in a=2, b=6, and c=-3


x+=+%28-6+%2B-+sqrt%28+36-4%282%29%28-3%29+%29%29%2F%282%282%29%29 Square 6 to get 36.


x+=+%28-6+%2B-+sqrt%28+36--24+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-3%29 to get -24


x+=+%28-6+%2B-+sqrt%28+36%2B24+%29%29%2F%282%282%29%29 Rewrite sqrt%2836--24%29 as sqrt%2836%2B24%29


x+=+%28-6+%2B-+sqrt%28+60+%29%29%2F%282%282%29%29 Add 36 to 24 to get 60


x+=+%28-6+%2B-+sqrt%28+60+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%28-6+%2B-+2%2Asqrt%2815%29%29%2F%284%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-6%2B2%2Asqrt%2815%29%29%2F%284%29 or x+=+%28-6-2%2Asqrt%2815%29%29%2F%284%29 Break up the expression.


x+=+%28-3%2Bsqrt%2815%29%29%2F%282%29 or x+=+%28-3-sqrt%2815%29%29%2F%282%29 Reduce


So the answers are x+=+%28-3%2Bsqrt%2815%29%29%2F%282%29 or x+=+%28-3-sqrt%2815%29%29%2F%282%29


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Jim