SOLUTION: Solve by using the quadratic formula. 3x^2 = 11x + 4

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Question 88263: Solve by using the quadratic formula. 3x^2 = 11x + 4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2+=+11x+%2B+4

3x%5E2+-+11x+-+4+=0+ Get everything to one side

Now let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general form of the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve 3%2Ax%5E2-11%2Ax-4=0 (notice a=3, b=-11, and c=-4)

x+=+%28--11+%2B-+sqrt%28+%28-11%29%5E2-4%2A3%2A-4+%29%29%2F%282%2A3%29 Plug in a=3, b=-11, and c=-4



x+=+%2811+%2B-+sqrt%28+%28-11%29%5E2-4%2A3%2A-4+%29%29%2F%282%2A3%29 Negate -11 to get 11



x+=+%2811+%2B-+sqrt%28+121-4%2A3%2A-4+%29%29%2F%282%2A3%29 Square -11 to get 121



x+=+%2811+%2B-+sqrt%28+121%2B48+%29%29%2F%282%2A3%29 Multiply -4%2A-4%2A3 to get 48



x+=+%2811+%2B-+sqrt%28+169+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)



x+=+%2811+%2B-+13%29%2F%282%2A3%29 Simplify the square root



x+=+%2811+%2B-+13%29%2F6 Multiply 2 and 3 to get 6

So now the expression breaks down into two parts

x+=+%2811+%2B+13%29%2F6 or x+=+%2811+-+13%29%2F6

Lets look at the first part:

x=24%2F6 Add the terms in the numerator
x=4 Divide

So one answer is
x=4
Now lets look at the second part:

x=-2%2F6 Subtract the terms in the numerator
x=-1%2F3 Divide

So another answer is
x=-1%2F3

So our solutions are:
x=4 or x=-1%2F3

Notice when we graph 3%2Ax%5E2-11%2Ax-4 we get:

+graph%28+500%2C+500%2C+-11%2C+14%2C+-11%2C+14%2C3%2Ax%5E2%2B-11%2Ax%2B-4%29+

and we can see that the roots are x=4 and x=-1%2F3. This verifies our answer