Algebra Demystified 2nd Ed

Chapter 10 QuadratiC EQuations 361

10. −−−=
    − −−−=−

++

10 34 12 0

1

2

10 34 12 1

2

0

5176

2

2

2

xx

xx

xx

()()

==

++=

+= +=

0

52 30

52030

()xx()

xx

−− 22   − 3 −−

=− =−

=−

3

52 3

2

5

xx

x

Extracting Roots

The second main approach to solve quadratic equations comes from the fact that

x^2 = k implies x = ± k. For instance, if x^2 = 9, then x = 3 or –3 because 3^2 = 9 and

()−= (^392). This method works best if the equation can be put in the form
ax^2 – c = 0, where c is not negative. We begin by solving for x^2 and then taking
the square root of each side of the equation. This method is sometimes called
extracting roots, or the square root method.
EXAMPLES
Solve the quadratic equation by extracting roots.
x^2 = 16
The equation is already written with x^2 isolated on one side, so we can
begin by taking the square root of each side.
x = ± 16
x = ± 4
Solve the quadratic equation by extracting roots.
3 x^2 = 27
Before we can take the square root of each side, we isolate x^2 , so we begin
by dividing each side of the equation by 3.
327
3
3
27
3
9
3
2
2
2
x
x
x
x
 = 
 = 
 = 
= ± 
EXAMPLES
Solve the quadratic equation by extracting roots.
x
EXAMPLES
Solve the quadratic equation by extracting roots.