Solving quadratic equationsFrom brackets, factorising and tacking it to the next level.

Solving quadratic equations from brackets.

Easy-peasy lemon squeeze Once there was a land where Mr wiggly

worm lived. One day Mr wiggly worm was out and about in his garden. When suddenly something dropped on his head. “oh my” Mr wiggly worm exclaimed. Mr wiggly worm looked down to find a quadratic equation in the form of a bracket. Mr wiggly worm picked up the brackets and he said “Mr wiggly worm will help with the bracket problem!

The end

This may be a simple and babyish story but I bet you when you are in your exam you will think about Mr wiggly worm.

So you ask “how to solve quadratic equations in bracket form. Well

First (x+3)(x+4)

Mr wiggly worm drew a grid of about… three by three.

(x+3)(x+4)

Then he split the brackets up and placed them in the grid. Mr wiggly worm’s grid looked like this

X +3x

+4

(x+3)(x+4)

The Mr wiggly worm had to work out what x*x was. He thought and thought… but he couldn't work it out. Do you know what x*x is? Click on the one you think it is.

2x x²

You got it! Continue

To bad. It was X². Carry on.

Mr wiggly worm’s grid looked like this

Mr wiggly worm did the same to the other bits of the brackets.

So his grid looked like this

x +3x x²

+4

x +3x x² +3x

+4 +4x 12

Mr wiggly worm sat down in his big arm chair. “is it all over yet?” he asked “no, Mr wiggly worm. Just one more thing to do!”

“we have to write it out!” Take the x²… Add the two x numbers to gather. 4x+3x=+7x And write out the last number. Mr wiggly worm only move diagonally from left to

right so we have to the same movement to write out our equation x +3

x x² +3x+4 +4x +12x²+7x+

12

See all done and so simple. Now to become a pro try these and don’t forget if you get stuck click on the question mark to see the power point again.

?

(x+3)(x+9)

(x+3)(x-15)

(x-2)(x-5)

(x+5)²

Factorising

It’s easy! You may look at an equation like: x²+2x-35 and think what do you want me to do

with that monster. But don’t worry I have created this power point to show you how to tame this monster.

Mr wiggly worm has a female friend called Miss Factorise. Miss Factorise moves backwards. She does the same thing that Mr Wiggly worm does but backwards!

First! x²+2x-35 Miss Factorise draws a little grid. Like

this

x²+2x-35 Now in the grid Miss Factorise can put

x². she know that x * x makes x² so she can put it into the grid as well. So Miss Factorises grid looks like this

xx x²

x²+2x-35 Now that she have dealt with the x² she

can cross it off or highlight it. Now Miss Factorise puts in the last

number. This is -35. Now her grid looks like this

xx x²

-35

x²+2x-35 Now the -35 has been put into the grid

she can cross it off or highlight it. “Here comes the hard part.” Miss

Factorise says. “You have to find the factors that add up

to +2 and multiple to get -35.” “Draw another table.” “Write out factors of 35” “And see if they add=A or multiple=M to get -35and +2” “7x-5 does the trick.”

7x5 M=35A=12

7x-5 M=-35A=2

-7x5 M=-35A=-2

So Miss Factorise can put the 7 in one box and the -5 in the other.

x 7x x²-5 -35

Just to finish the grid off Miss Factorise multiplies. 7*x and -5*x. So her grid looks like this

x 7x x² 7x-5 -5x -35

To finish “To finish take the top and left side rows

and put them into brackets. Like this (x+7)(x-5)”

x 7x x² 7x-5 -5x -35

Your turn

To become a pro at factorising try these and if you need help click in the question mark to see the power point again.

?

x²+8x+15

x²-4x-32

x²-9x-22

x²-7x+12m²-m-12

(x+3)(x+3)

The next level! Well clever clogs! You have reached the

final hurdle. Weather you succeed or not is up to weather you are awake to day. Which I’m sure you are. So step forward and just finish the power point!

Go on click!!!

All of these are very similar to the question you have been show. However these have a slight twist.

All this means is that there are two of the same bracket. So instead of (x+3) it is(x+3)(x+3) and then you know how to do the rest.

(x+3)²

(3x+4)(4x+2) This is simple. Instead of having just x*x

you would have 3x*4x which you know to be 12x². And then it’s the same way of working it out.

m²-m-12 You may think: HU?!?!?! but once you get

over the letter change and that m is in fact 1m you can work it out much easily.

Say we change it to: x²-1x-12 could you work that out. Well it’s

the same. So DO NOT PANIC!

Smarty pants! You know the drill. You try and if you need help

click on the bit you need help with.

From brackets Factorising The next level

(5p+2)(3p+2)

(3a+4)(a-2)

5q²-17q+6

3k²+k-6

Good luck for you Exam!