A quadratic equation can be solved using any of the methods below;

• Factorization method
• Formula method
• Completing the square method

1. Factorization method

In this method we make use of the fact that, if A.B = 0, it implies A=0 or B=0. E.g.

Solve the following quadratic equations by using factorization method;

1. X²-5x+6=0
2. X²-x-20=0

Solution

1. (X²+-3x) +(-2x+6)=0                  2) (x²+-5x) +(4x-20)=0

x(x-3) -2(x-3)=0                              x(x-5) +4(x-5)=0

X-2=0, x-3=0                                    x+4=0, x-5=0

X= 2, X= 3                                           x= -4,  x= 5

2. Formula method

To solve a quadratic equation of the form ax²+bx+c=0 (where a is not equal to 0), we can make use of the formula below;

x=  -b±b2-4ac2a

Example

1. X²-5x+6=0
2. X²-x-20=0

Solution

1. a=1, b=-5, c=6                          2) a=1, b=-1, c=-20

x= --5±(-5)2-4(1)(6)21                x= --1±(-1)2-4(1)(-20)21

x = -(-5)±12=5±12                        x= 1±812=1±92

x=62=3,  x=42=2                      x=102 , x=82

x=3, x=2                                            x=5, x=4

3. By completing the square

In this section we shall solve quadratic equations of the form,

X² – a²=0

Example

1. x²-4=0
2. 4x²-9=0

Solution

1. X² -4=0                                        2) 4X² = 9

X² = 4                                                X² = 94

Taking square roots on both side

X =±4                                             X = ±94

X = ±2                                                X= ±32

X=2, x=-2                                             X= 32 , X= -32