Solving Problems Using Simultaneous Equations

Solving Quadratic Equations

Let's have a look at how we solve a quadratic equation:

x²-3x+2=0

The easiest way to solve them is to follow certain steps:

Step 1

Find two numbers where when they are multiplied together equal the firstnumber (a=1) multiplied by the third number (c=2). These two numbers when addedto each other must also equal the second number (b=-3).

In the above example, the solution is -2 and -1.
We can see that when added together the result is -3 and that when multiplied together, the result is 2

Step 2

Rewrite the original equation splitting the middle part into two using thenumbers which you found in step 1.

x²-x-2x+2=0

Step 3

Start to factorise both halves of the equation:

x(x-1)-2(x-1)=0

At this point you will know if you are going along the correct track if thefirst bracket is the same as the second bracket.

Step 4

Collect everything before each bracket and put it into one bracket andmultiply this bracket by that which is inside the identical brackets:

(x-1)(x-2)=0

Step 5

In order for the left side of the equation to be equal to 0, one of the twobrackets must equal 0. So either:

a.
x-1=0
x=1

b
x-2=0
x=2

Step 6

Check these answers:

1²-(3*1)+2=0
1-3+2=0
0=0

2²-(3*2)+2=0
4-6+2=0
0=0

Therefore the possible solutions for the above equation are confirmed to be 1 and 2