Algebra Demystified 2nd Ed

Chapter 10 QuadratiC EQuations 363

2. 64 − x^2 = 0
   64 = x^2
   ± 8 = x


3. 4 x^2 = 100
   x^2 =^100
   4
   x^2 = 25
   x = ± 5


4. 2 x^2 = 3
   x^2 =^3
   2

x = ±^3

2

x = ±^3

2

2

2

⋅

x = ±^6

2

5. 
   

   −6x^2 = −80
   x^2 = –

   
   

80

6

x^2 =^40

3

x = ±^40

3

x  = ±=^40  ±

3

3

3

120

3

⋅

x  = ±=^430  ±

3

230

3

⋅

Solving Quadratic Equations with the Quadratic Formula

The first two methods we used for solving quadratic equations only work for

equations that are factorable or where one side is written as a perfect square.

The last method that we will learn works to solve any quadratic equation. This

method for solving quadratic equations comes from the fact that x^2 = k implies

xk=−,.k Using this fact and a technique called completing the square, the