SOLUTION: Solve. x^2 + 1 = 17

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Question 88254: Solve. x^2 + 1 = 17
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+1+=+17

x%5E2+%2B+1+-+17=0 Subtract 17 from both sides

x%5E2++-16=0 Combine like terms

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%2B0%2Ax-16=0 (notice a=1, b=0, and c=-16)

x+=+%28-0+%2B-+sqrt%28+%280%29%5E2-4%2A1%2A-16+%29%29%2F%282%2A1%29 Plug in a=1, b=0, and c=-16



x+=+%28-0+%2B-+sqrt%28+0-4%2A1%2A-16+%29%29%2F%282%2A1%29 Square 0 to get 0



x+=+%28-0+%2B-+sqrt%28+0%2B64+%29%29%2F%282%2A1%29 Multiply -4%2A-16%2A1 to get 64



x+=+%28-0+%2B-+sqrt%28+64+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-0+%2B-+8%29%2F%282%2A1%29 Simplify the square root



x+=+%28-0+%2B-+8%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-0+%2B+8%29%2F2 or x+=+%28-0+-+8%29%2F2

Lets look at the first part:

x=8%2F2 Add the terms in the numerator
x=4 Divide

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

x=-8%2F2 Subtract the terms in the numerator
x=-4 Divide

So another answer is
x=-4

So our solutions are:
x=4 or x=-4

Notice when we graph x%5E2%2B0%2Ax-16 we get:

+graph%28+500%2C+500%2C+-14%2C+14%2C+-14%2C+14%2C1%2Ax%5E2%2B0%2Ax%2B-16%29+

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