Need help with this one: Please Explain ( Algebra)?

Question

If x^2 -2x-8= 0, then x=

# 2

Simplify: x^2 -x-6
--------------------------
x^2-2x-3



Thanks

Answer 1

x = 4, -2

Use the quadratic equation: {-b +/- (b^2 - 4ac)^0.5} / 2a. a = 1, b = -2, c = -8.

Answer 2

What you need to do is find factors of -8 that, when added, will sum to -2 (you could use the quadratic formula, but it's really not necessary in this case).

You can break down x²-2x-8 into two expressions, so

x²-2x-8 = (x+n1)(x+n2), where n1 and n2 could be positive or negative.

I'll give you another example, from which you should be able to figure out the answer to your question:

x²-x-6 = 0,

so I need factors of -6 that will add to produce -1. How about -3 and +2?

We now have (x-3)*(x+2) = 0. Using the FOIL method on the left side of the equation, you can see that this mutiplies out to x²-x-6. In this case,

x = 3, and x=-2.

Use this approach for x²-2x-8. Good luck.

Answer 3

There are a number of ways to complete this problem.

Because of its simplicity, I would recommend doing this pronlem by completing the square.

x² - 2x - 8 = 0

(x² - 2x + (-2/2)²) - 8 - (-2/2)² = 0

(x² - 2x + 1) - 8 - 1 = 0

(x-1)² - 9 = 0

x - 1 = √(9)

x - 1 = ± 3

x = ± 3 + 1

x = 4 or -2

Answer 4

x^2 -2x - 8 =0

First factor since -4 times 2 gives -8, then factors are

(x-4)(x+2) = 0 since this also gives the correct mioddle term.

now since you have a product that = 0 then at least one of the factors is 0. Thus either x-4=0 and x=4 or
x+2=0 and x=-2. A quick check in the original equation will show that both are true.

Answer 5

first you need to factor the equation by finding the factors of 8 that have a difference of 2 because the middle term is 2 and the sign on the 8 is negative (subtraction)
8=4*2 and 4-2=2 so the factors of 8 to use are 4 and 2

the equation now factors into 2 binomials and since the middle term in the equation is negative, the negative in the binomials goes with the larger factor (4):
x^2-2x-8 = (x-4)(x+2) = 0

now set each of the factored terms =0
x-4=0
x=4
and
x+2=0
x=-2

Answer 6

if x^2-2x-8 = 0
this is a quadratic
[-b +- Sqrt( b^2 - 4ac)]/2a

therefore
[2+- Sqrt(4+32)]2
[2+-6]/2
1+-3
the answers are 4 and -2

Answer 7

1.(x-4)(x+2)
so x=4,-2
2.(x-3)(x+2)
so x=3,-2
3.(x-3)(x+1)
so x=3,-1

Answer 8

x² = 2x - 8 = 0

x² - 4x + 2x - 8 = 0

x(x - 4) + 2(x - 4) = 0

(x + 2)(x - 4)

- - - - - - - -s-

Answer 9

1. (x-4)(x+2)
x=-2,4

2. (x-3)(x+2)
--------------
(x-3)(x+1)

The x-3 cancels out on the top and bottom.

x+2
-----
x+1

That is your final answer.