IXL - Complete the square (Algebra 1 practice)

or

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

t² + 12t +

ref_doc_title.

or

Learn with an example

question

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

m² + 10m +

key idea

With
quadratic
expressions
like
x ²
+
b x ,
you
can
complete
the
square
by
adding
b
2
²
.

solution

Add
b
2
²
to
complete
the
square.

m

²

+

10

m

+

b

2

²

Plug in b = 10

=

m

²

+

10

m

+

10

2

²

Plug in b = 10

Divide

=

m² + 10m + 5²

Divide

Square

=

m² + 10m + 25

Square

This
quadratic
can
be
written
as
a
square,
(m + 5)²
,
so
it
is
a
perfect-square
quadratic.
The
number
needed
to
complete
the
square
was
25
.

Looking for more? Try these:

Lesson: Completing the square

or

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Teacher tools

Work it out

Not feeling ready yet? These can help:

X.7Factor quadratics: special cases

R.1Powers with integer bases

P.15Divide integers

R.2Powers with decimal and fractional bases

Lesson: Completing the square