d+ 2d - 8 = 0

Question

 

How do I solve this equation

d square + 2d - 8 = 0

Answer 1

d² + 2d - 8 = 0

This equation can be solved by factoring.  You need to look for factors of -8 that add up to 2. (In any equation of the form x² + bx + c = 0, you look for factors of c that add up to b).  In this case, 4 and -2 add up to 2; therefore the factors of d² + 2d - 8 are (d+4)(d-2).

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

Using the zero product rule, this equation can now be separated into two seperate equations:

d+4=0   and   d-2=0

Subtract 4 from both sides of the first equation and you get d = -4.  Add 2 to both sides of the second equation and you get d = 2.  Therefore your solution set is {-4, 2}.

 

Answer 2

If you aren't good at factoring, using the quadratic equation would get you the same result.

Answer 3

As has been noted above, the problem can be solved both factoring and the quadratic formula.  If you can't factor or remember the formula, you can also solve it using a process called completing the square.

First, divide the equation through by a, and subtract c from both sides.  In this case, it will look like this:

d^2+2d=8

Then add the square of half of b to each side.  b=2, so half of b is 1 and 1 squared is still one.  Adding 1 to both sides gives:

d^2+2d+1=9

You can then take the square root of both sides and get d+1=3 and d+1=-3.  The answers come out to -4 and 2 like they did for everyone else.

Side Note: Completing the square on the generic equation ax^2+bx+c=0 will get you the quadratic formula :)

Answer 4

First place the equation i the standard format of ax²+bx+c. Your equation d² + 2d - 8 = 0 is already in this format. Cool, now you need to find the product of the end terms (ac) = (1)(-8) = -8

Find the factos of -8 so that their sum adds up to the center term (b)= 2

(-4) X 2 = -8 , but their sum -4+2 = -2

4 X (-2) = -8 and also their sum = 4 + (-2) = 4-2 = 2

So let us choose 4 and -2 as our factors

Split the center term on these basis (2d = 4d - 2d)

d² + 2d - 8 = 0

d² + 4d - 2d - 8 = 0

Factor our d from the first two terms and 2 from the second two terms

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

Factor out (d+4) from both ther terms

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

There fore d+ 4 = 0  (OR)  d -2 = 0

d = -4 or d = 2   are the roots and it can be shown in the solution set as {-4, 2}