Solving Quadratics By Factoring Worksheet - Chapter 14-1 Page 7
ADVERTISEMENT
1
2
3
4
5
6
7374
◆
Chapter 14
Quadratic Equations
14–2
Solving Quadratics by Completing the Square
If a quadratic equation is not factorable, it is possible to manipulate it into factorable form by a
procedure called completing the square. The form into which we shall put our expression is the
perfect square trinomial, Eqs. 47 and 48, which we studied in Sec. 8–6.
In the perfect square trinomial,
The method of completing the
1. The fi rst and last terms are perfect squares.
square is really too cumbersome
2. The middle term is twice the product of the square roots of the outer terms.
to be a practical tool for solving
quadratics. The main reason we
To complete the square, we manipulate our given expression so that these two conditions
learn it is to derive the quadratic
are met. This is best shown by an example.
formula. Furthermore, the
method of completing the square
is a useful technique that we’ll
2
◆◆◆
Example 12:
Solve the quadratic x
8x
6
0 by completing the square.
use again in later chapters.
Solution:
Subtracting 6 from both sides, we obtain
x
2
8x
6
We complete the square by adding the square of half the coeffi cient of the x term to both sides.
The coeffi cient of x is
8. We take half of
8 and square it, getting ( 4)
2
or 16. Adding 16 to
both sides yields
x
2
8x
16
6
16
10
Factoring, we have
2
(x
4)
10
Taking the square root of both sides, we obtain
x
4
10
Finally, we add 4 to both sides.
x
4
10
◆◆◆
7.16 or 0.838
When you are adding the quantity needed to complete the
square to the left-hand side, it's easy to forget to add the same
Common
quantity to the right-hand side.
Error
2
x
8x
6
16
16
don’t forget
2
If the x
term has a coeffi cient other than 1, divide through by this coeffi cient before com-
pleting the square.
◆◆◆
Example 13:
Solve:
2
2x
4x
3
0
Solution:
Rearranging and dividing by 2 gives
3
2
x
2x
2
ADVERTISEMENT
0 votes
Related Articles
Related forms
Solving Quadratic Equations By Factoring Worksheet With Answer Key - Tallahassee Community College
Education
Solving Quadratic Equations By Factoring Worksheet With Answers - Algebra 2, Glencoe Mcgraw-hill
Education
Related Categories
Parent category: Education