SOLUTION: Solve. x^2 – 7x – 4 = 0

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Question 88260: Solve. x^2 – 7x – 4 = 0

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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 x%5E2-7%2Ax-4=0 (notice a=1, b=-7, and c=-4)

x+=+%28--7+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A-4+%29%29%2F%282%2A1%29 Plug in a=1, b=-7, and c=-4



x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A-4+%29%29%2F%282%2A1%29 Negate -7 to get 7



x+=+%287+%2B-+sqrt%28+49-4%2A1%2A-4+%29%29%2F%282%2A1%29 Square -7 to get 49



x+=+%287+%2B-+sqrt%28+49%2B16+%29%29%2F%282%2A1%29 Multiply -4%2A-4%2A1 to get 16



x+=+%287+%2B-+sqrt%28+65+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%287+%2B-+sqrt%2865%29%29%2F%282%2A1%29 Simplify the square root



x+=+%287+%2B-+sqrt%2865%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%287+%2B+sqrt%2865%29%29%2F2 or x+=+%287+-+sqrt%2865%29%29%2F2


Which approximate to

x=7.53112887414927 or x=-0.531128874149275


So our solutions are:
x=7.53112887414927 or x=-0.531128874149275

Notice when we graph x%5E2-7%2Ax-4 we get:



when we use the root finder feature on a calculator, we find that x=7.53112887414927 and x=-0.531128874149275.So this verifies our answer