IXL - Solve a quadratic equation by completing the square (Algebra 2 practice)

Solve by completing the square.

m² − 28m − 31 = 0

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

m = or m =

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Learn with an example

question

Solve by completing the square.

f² − 12f = ^–19

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

f = or f =

key idea

With quadratic equations (ax² + bx + c = 0), you can solve by completing the square.

Step 1: Make sure that the left side of the equation looks like x² + bx.

Step
2:
Add
b
2
²
to
both
sides.

Step
3:
Factor
the
left
side
as
x
+
b
2
²
.

Step 4: Take the square root and solve.

solution

Step 1: Make sure that the left side of the equation looks like x² + bx.

This step does not apply, because the left side of the equation already looks like x² + bx.

f² − 12f

^–19

Step
2:
Add
b
2
²

to
both
sides.

Since
b
=
^–12 ,
b
2
²

=
^–12
2
²

=
( ^–6 )
²

= 36
.
Add
36
to
both
sides.

f² − 12f + 36 = 17

Step
3:
Factor
the
left
side
as
x
+
b
2
²

.

In
general,
an
expression
of
the
form
x
²

+
b
x
+
b
2
²
can
be
factored
as
x
+
b
2
²
.

The
expression
f² − 12f + 36
is
of
this
form,
with
b
=
^–12 .
So,
it
can
be
factored
as
(f − 6)²
.

Rewrite the equation with the left side factored.

(f − 6)² = 17

Step 4: Take the square root and solve.

Take the square root

f − 6

≈

±4.12

Take the square root

Add
6
to
both
sides

≈

6 ± 4.12

Add
6
to
both
sides

Split ± into + or -

≈

6 + 4.12 or f ≈ 6 − 4.12

Split ± into + or -

Simplify

≈

10.12 or f ≈ 1.88

Simplify

Looking for more? Try these:

Lesson: Completing the square

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Teacher tools

Work it out

Not feeling ready yet? These can help:

O.4Complete the square

E.1Square roots of perfect squares

Lesson: Completing the square

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