What are the steps of quadratic equation by copying the equation?

Answer 1

okay. so say if the question is:

Solve the quadratic:

x2 + 8x + 15 = 0

STEP 1 (skip if you know how to factorise quadratics)

factorise. As it is x2 , your brackets should both start with x.

(x ) (x )

Now you need two numbers that will add to make 8 and multiply to make 15. The two numbers are 5 and 3. Let's check them

5 x 3 = 15

5 + 3 = 8

Correct. So we stick them in our brackets. 8 and 15 are both positive, so, the factorised brackets will be:

(x + 5) (x + 3) = 0

STEP 2

Now, if (x + 5) (x + 3) = 0, this must mean that either the first, or second bracket must equal 0.

So, the next step to write out is:

x + 5 = 0 x + 3 = 0

STEP 3

Then, rearrange to find x, so

x = -5 x = -3

So, your working out should look like this.

x2 + 8x + 15 = 0

(x + 5) (x + 3) = 0

x + 5 = 0 x + 3 = 0

x = -5 x = -3

So that's how, there are different types of quadratic equation, the main thing is to know how to factorise and have all of your terms on one side so that it equals 0. After that, it's really easy. See if you get these examples, which are different types of quadratic. If you get them, you're good to go! If not, then... we'll get to that later.

Solve x2 - 4 = 0.

This quadratic has just two terms, and nothing factors out of both, so it's a difference of squares (so I can factor) or it can be reformatted as "(squared part) equals (a number)" so I can square-root both sides. In this case, I can factor:

x2 - 4 = 0

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

x + 2 = 0 or x - 2 = 0

x = -2 or x = 2

Solve x2 - 7x = 0opyright © Elizabeth Stapel 2002-2011 All Rights Reserved

x2 - 7x = 0

x(x - 7) = 0

x = 0 or x - 7 = 0

x = 0 or x = 7

Solve x2 - 4 = 0

x2 - 4 = 0

x2 = 4

x = 2

Solve 3x2 + 8x + 5 = 0.

There are different ways to solve this, but this is how I do it. The reason why its different is because the number infront of the x2 is not 1.

So first, I call each of the numbers a b and c. So

a= 3

b= 8

c = 5

I need 2 numbers that multiply to give ac ( which is 15)

And add to give b which is 8.

These numbers are 3 and 5.

Let's check them:

3 + 5 = 8

3 x 5 = 15

We now use 3 and 5 to split up 8x

So we get

3x2 + 3x + 5x + 5 = 0

Now, we split them up and factorise the first to terms and the last two terms.

3x2 + 3x 5x + 5

3x(x + 1) 5( x + 1)

The two brackets should be the same. Next we use the numbers outside the brackets (that's 3x and 5) as our other bracket. So we get

(x +1) (3x + 5) = 0 and now we solve.

x + 1 = 0 3x + 5 = 0

x = -1 3x = -5

x = -5/3

If you don't use this method, that's fine, but I thought it would be worth putting it in.

I really hope this helps! Sorry if it makes no sense at all :)