IXL - Solve a quadratic equation by completing the square (Algebra 1 practice)

Solve by completing the square.

r² − 2r = 13

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

r = or r =

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Learn with an example

question

Solve by completing the square.

d² − 14d = 3

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

d = or d =

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.

d² − 14d

Step
2:
Add
b
2
²

to
both
sides.

Since
b
=
^–14 ,
b
2
²

=
^–14
2
²

=
( ^–7 )
²

= 49
.
Add
49
to
both
sides.

d² − 14d + 49 = 52

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
d² − 14d + 49
is
of
this
form,
with
b
=
^–14 .
So,
it
can
be
factored
as
(d − 7)²
.

Rewrite the equation with the left side factored.

(d − 7)² = 52

Step 4: Take the square root and solve.

Take the square root

d − 7

≈

±7.21

Take the square root

Add
7
to
both
sides

≈

7 ± 7.21

Add
7
to
both
sides

Split ± into + or -

≈

7 + 7.21 or d ≈ 7 − 7.21

Split ± into + or -

Simplify

≈

14.21 or d ≈ ^–0.21

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:

Z.4Complete the square

A.8Square roots

C.7Solve one-step linear equations

X.3Factor out a monomial

Lesson: Completing the square

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