x^2 - 4x - 5 = 0?

Answer 1

x^2 - 4x - 5 = 0
(x - 5)(x + 1) = 0

x - 5 = 0
x - 5 + 5 = 0 + 5
x = 5

x + 1 = 0
x + 1 - 1 = 0 - 1
x = -1

x = (5, -1)

Answer 2

You have to factor this one, I assume. Or, perhaps, you have to find x. I will show you how to do both.

Think about FOIL. It can be used to multiply two binomials, usually producing a trinomial such as yours. So, if you factor the equation and come up with two binomials, you can use FOIL to check your answer.

x^2 - 4x - 5 = 0

This can be factored into two binomials like so:
(x +- _) (x +- _)

I put in the x's because, in FOIL, x times x is x^2, the first part of your trinomial.

Right now we don't know if we have to add or subtract the constants, and we don't know what those constants are. So, think about what could go in the blanks above. Whatever they are, they have to be multiplied together to get 5.

Since 5 is a prime number, its only factors are 1 and 5. We can put those numbers in, but now we still don't know whether to add or subtract. So I'll leave those blank below:

(x _1) (x _ 5)

To get -5 at the end of the trinomial, one and only one of the factors can have a minus sign. If there were two negatives or two positives, you'd end up with +5 at the end (think about the L in FOIL).

Adding up the O and I in FOIL gives us -4. The only way to get -4 from 1 and 5 here is to make 5 negative and 1 positive. So you'll end up with

(x +1) (x - 5)

which multiplies out to

x^2 -4x -5

Which is the problem we started out with. So congratulations, we factored it!

Now, to find x, you could just put the old equation into the quadratic formula, but it is much easier to just use our factors.

(x +1) (x - 5) = 0

What values could we substitute for x to make this expression equal 0? If we had x = -1, the left binomial would simplify to 0, and multiplying (x-5) times 0 makes 0.

Similarly, if x = 5, the same thing would happen.

So your answer is that x = -1 or +5. I hope that helps!

Answer 3

x^2 - 4x - 5 = 0
( x - 5 ) ( x + 1 ) = 0
x-5 = 0 and x + 1 = 0
x = 5 and x = -1

Answer 4

x= 5,-1

Answer 5

x^2-4x-5=0
(x+1)(x-5)=0
Two solutions: x= -1 and x= 5

Answer 6

(x-5)(x+1)
x=5 or x=-1

Answer 7

(x-5) (x+1)

Answer 8

factor

look for two numbers that multiply to -5 and add to -4

the two numbers are -5 and 1

since the leading coefficient is 1, just plug the two numbers in

(x - 5) (x + 1) = 0
x = 5 or -1

Answer 9

1) Quadratic formula
2) By inspection: product is -5, sum is -4. Try

(x + 1)(x - 5) = 0

and solve for x.

Answer 10

ok there is no way it can b -1 and 5 because that wouldnt give u the -4 in the equation...it has to be -5,1 and i guess some ppl should learn 2 factor since so many ppl got it wrong.