SOLUTION: Solve the equation: y^2 - 2y -24 = 0

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Question 96250: Solve the equation:
y^2 - 2y -24 = 0
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 y:


Starting with the general quadratic

ay%5E2%2Bby%2Bc=0

the general solution using the quadratic equation is:

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

So lets solve y%5E2-2%2Ay-24=0 ( notice a=1, b=-2, and c=-24)

y+=+%28--2+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A-24+%29%29%2F%282%2A1%29 Plug in a=1, b=-2, and c=-24



y+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A-24+%29%29%2F%282%2A1%29 Negate -2 to get 2



y+=+%282+%2B-+sqrt%28+4-4%2A1%2A-24+%29%29%2F%282%2A1%29 Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because %28-2%29%5E2=-2%2A-2=4.)



y+=+%282+%2B-+sqrt%28+4%2B96+%29%29%2F%282%2A1%29 Multiply -4%2A-24%2A1 to get 96



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



y+=+%282+%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)



y+=+%282+%2B-+10%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

y+=+%282+%2B+10%29%2F2 or y+=+%282+-+10%29%2F2

Lets look at the first part:

x=%282+%2B+10%29%2F2

y=12%2F2 Add the terms in the numerator
y=6 Divide

So one answer is
y=6



Now lets look at the second part:

x=%282+-+10%29%2F2

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

So another answer is
y=-4

So our solutions are:
y=6 or y=-4

Notice when we graph x%5E2-2%2Ax-24 (just replace y with x), we get:

+graph%28+500%2C+500%2C+-14%2C+16%2C+-14%2C+16%2C1%2Ax%5E2%2B-2%2Ax%2B-24%29+

and we can see that the roots are y=6 and y=-4. This verifies our answer