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

Solve by completing the square.

m² − 4m = 49

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.

p² + 8p = ^–13

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

p = or p =

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.

p² + 8p

^–13

Step
2:
Add
b
2
²

to
both
sides.

Since
b
=
8,
b
2
²

=
8
2
²

=
4 ²

= 16
.
Add
16
to
both
sides.

p² + 8p + 16 = 3

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
p² + 8p + 16
is
of
this
form,
with
b
=
8.
So,
it
can
be
factored
as
(p + 4)²
.

Rewrite the equation with the left side factored.

(p + 4)² = 3

Step 4: Take the square root and solve.

Take the square root

p + 4

≈

±1.73

Take the square root

Subtract
4
from
both
sides

≈

^–4 ± 1.73

Subtract
4
from
both
sides

Split ± into + or -

≈

^–4 + 1.73 or p ≈ ^–4 − 1.73

Split ± into + or -

Simplify

≈

^–2.27 or p ≈ ^–5.73

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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