solve the equation.

Question

23d=-10-6d^2

Answer 1

To answer this, first you must set it equal to 0 and use factoring or the quadratic formula.

By setting it equal to 0, you get: 

 

6d^2+23d+10 =0

 

Now, you can choose how you would like to solve it. Either factoring or the quadratic formula. I would prefer to factor it. If you factor, you must figure out what multiplies to the first and last numbers multiplies and adds to the middle number. In other words, what multiplies to 60 and adds to 23? Of course, the answers is 20 and 3. Now that you have found the factors, you can write 23d as 20d +3d. And the equation looks like this.

 

6d^2+3d+20d+10 =0

 

Now, you must factor by grouping. That is, taking the largest number (3) and varible (d) from the first two terms. And this is done again for the third and fourth term. Making the equation look like this:

 

3d(2d+1) +10(2d+1) = 0

 

Now, you can factor this again because each term has '2d+1' Thus, you can factor that out, leaving us with the factors. 

 

(3d+10)(2d+1)= 0

 

Now, if two things multiplied equals 0, either or both of them can be 0. Thus, you must separate the factors and solve. Like this...

 

3d+10 =0

 

3d=-10

 

d=-10/3

 

and 

 

2d+1 = 0

 

2d = -1

 

d= -1/2

 

Thus, the answers that satisfy this equation for d = -10/3 and -1/2

 

Best of luck. :)