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

Solve by completing the square.

q² + 20q + 21 = 0

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

q = or q =

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Learn with an example

question

Solve by completing the square.

f² + 10f − 7 = 0

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.

To make the left side of the equation look like x² + bx, add 7 to both sides.

f² + 10f − 7

f² + 10f

Step
2:
Add
b
2
²

to
both
sides.

Since
b
=
10,
b
2
²

=
10
2
²

=
5 ²

= 25
.
Add
25
to
both
sides.

f² + 10f + 25 = 32

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 + 10f + 25
is
of
this
form,
with
b
=
10.
So,
it
can
be
factored
as
(f + 5)²
.

Rewrite the equation with the left side factored.

(f + 5)² = 32

Step 4: Take the square root and solve.

Take the square root

f + 5

≈

±5.66

Take the square root

Subtract
5
from
both
sides

≈

^–5 ± 5.66

Subtract
5
from
both
sides

Split ± into + or -

≈

^–5 + 5.66 or f ≈ ^–5 − 5.66

Split ± into + or -

Simplify

≈

0.66 or f ≈ ^–10.66

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

Lesson: Completing the square

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