SOLUTION: Can someone please show me how this is done. The way I am doing it the teacher says is incorrect. x^2 - 4x - 60 = 0

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Question 151224: Can someone please show me how this is done. The way I am doing it the teacher says is incorrect.
x^2 - 4x - 60 = 0
Found 2 solutions by jim_thompson5910, jojo14344:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Here are two ways to solve this problem


Method #1 Quadratic Formula (preferred method):


x%5E2-4x-60=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-4, and c=-60


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%28-60%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-4, and c=-60


x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%28-60%29+%29%29%2F%282%281%29%29 Negate -4 to get 4.


x+=+%284+%2B-+sqrt%28+16-4%281%29%28-60%29+%29%29%2F%282%281%29%29 Square -4 to get 16.


x+=+%284+%2B-+sqrt%28+16--240+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-60%29 to get -240


x+=+%284+%2B-+sqrt%28+16%2B240+%29%29%2F%282%281%29%29 Rewrite sqrt%2816--240%29 as sqrt%2816%2B240%29


x+=+%284+%2B-+sqrt%28+256+%29%29%2F%282%281%29%29 Add 16 to 240 to get 256


x+=+%284+%2B-+sqrt%28+256+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%284+%2B-+16%29%2F%282%29 Take the square root of 256 to get 16.


x+=+%284+%2B+16%29%2F%282%29 or x+=+%284+-+16%29%2F%282%29 Break up the expression.


x+=+%2820%29%2F%282%29 or x+=++%28-12%29%2F%282%29 Combine like terms.


x+=+10 or x+=+-6 Simplify.


So our answers are x+=+10 or x+=+-6



Method #2 Factoring:

x%5E2-4x-60=0 Start with the given equation

%28x-10%29%28x%2B6%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x-10=0 or x%2B6=0

x=10 or x=-6 Now solve for x in each case


So our answers are

x=10 or x=-6


Notice if we graph y=x%5E2-4x-60 we can see that the roots are x=10 and x=-6 . So this visually verifies our answer.


+graph%28500%2C500%2C-10%2C12%2C-10%2C10%2C0%2C+x%5E2-4x-60%29+



Note: even though the factoring method may seem easier, it does not work for every quadratic.

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 - 4x - 60 = 0
=%28x-10%29%28x%2B6%29=0} ---------------> its a perfect square
If you want quadratic formula its up to you,
a=1, b=-4, c=-60
=x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
*Plug the given and you'll get the same answer
Thank you,
Jojo