SOLUTION: x2+4x-21=0 trying to find the two solutions??? I was fine till c was a value... when c = o I had no problems solving now that c = a value.. im stuck help i can get this far: a

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Question 139775: x2+4x-21=0
trying to find the two solutions??? I was fine till c was a value... when c = o I had no problems solving now that c = a value.. im stuck help i can get this far:
a=1
b=4
c= -21 -4+_ 4sqd + 4(1)(-21) divided by 2(1)

then, -4+- 4sqd + -84 divided by 2
then i get confused.... help






Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's use the quadratic formula to solve for x:


Starting with the general quadratic

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

the general solution using the quadratic equation is:

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



So lets solve x%5E2%2B4%2Ax-21=0 ( notice a=1, b=4, and c=-21)




x+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A1%2A-21+%29%29%2F%282%2A1%29 Plug in a=1, b=4, and c=-21



x+=+%28-4+%2B-+sqrt%28+16-4%2A1%2A-21+%29%29%2F%282%2A1%29 Square 4 to get 16



x+=+%28-4+%2B-+sqrt%28+16%2B84+%29%29%2F%282%2A1%29 Multiply -4%2A-21%2A1 to get 84



x+=+%28-4+%2B-+sqrt%28+100+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-4+%2B-+10%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-4+%2B-+10%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-4+%2B+10%29%2F2 or x+=+%28-4+-+10%29%2F2

Lets look at the first part:

x=%28-4+%2B+10%29%2F2

x=6%2F2 Add the terms in the numerator
x=3 Divide

So one answer is
x=3



Now lets look at the second part:

x=%28-4+-+10%29%2F2

x=-14%2F2 Subtract the terms in the numerator
x=-7 Divide

So another answer is
x=-7

So our solutions are:
x=3 or x=-7

Notice when we graph x%5E2%2B4%2Ax-21, we get:

+graph%28+500%2C+500%2C+-17%2C+13%2C+-17%2C+13%2C1%2Ax%5E2%2B4%2Ax%2B-21%29+

and we can see that the roots are x=3 and x=-7. This verifies our answer