Algebra 1 Common Core Student Edition, Grade 8-9

Completing the Square

Co m m o n Co r e St a t e St a n d a r d s

A-REI.B.4a Use the method o f com pleting the square

to transform any quadratic equation in x in to an

equation o f the form {x- p)2 = q ... Also A-REI.A.1,

A-REI.B.4b

MP 1, IVIP 2, M P3. M P4

Objective To solve quadratic equations by completing the square

Get t i n g Re ad y!

Your school has a field with an a re a

of 8400 yd2. The football coach is

planning to section o f f th e field to run

a variety of practice drills. W hat is

Factoring is only (^) th e value of x? Explain your reasoning.
one way to solve a
quadratic equation.
In th is lesson, you'l
lea rn a n o t h e r w ay.
v. ,U
MAtHEMAtiCAL *n previous lessons, you solved quadratic equations by finding square roots and by
PRACTICES factoring. These methods work in some cases, but not all.
Lesso n
Vocabulary
com pleting th e
square
Essent ial Und er st and ing You can solve any quadratic equation by first writing
it in the form m2 = n.
You can model this process using algebra tiles. The algebra
tiles at the right represent the expression x2 + 8x.
Here is the same expression rearranged
to form part of a square. Notice that the
x-tiles have been split evenly into two
groups of four.
You can complete the square
by adding 42, or 16,1-tiles. The
completed square is x2 + 8x+ 16,
or (x + 4)2.
In general, you can change the expression x2 + bx into a perfect-square trinomial by
adding (|) to x2 + bx. This process is called com pleting the square. The process is
the same whether b is positive or negative.
576 Ch ap t e r 9 Quadratic Functions and Equations
Lilt