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

Solve by completing the square.

4x² − 88x − 116 = 0

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

x = or x =

ref_doc_title.

Learn with an example

question

Solve by completing the square.

4z² − 80z + 76 = 0

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

z = or z =

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, subtract 76 from both sides and divide by 4.

4z² − 80z + 76

4z² − 80z

^–76

z² − 20z

^–19

Step
2:
Add
b
2
²

to
both
sides.

Since
b
=
^–20 ,
b
2
²

=
^–20
2
²

=
( ^–10 )
²

= 100
.
Add
100
to
both
sides.

z² − 20z + 100 = 81

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
z² − 20z + 100
is
of
this
form,
with
b
=
^–20 .
So,
it
can
be
factored
as
(z − 10)²
.

Rewrite the equation with the left side factored.

(z − 10)² = 81

Step 4: Take the square root and solve.

Take the square root

z − 10

±9

Take the square root

Add
10
to
both
sides

10 ± 9

Add
10
to
both
sides

Split ± into + or -

10 + 9 or z = 10 − 9

Split ± into + or -

Simplify

19 or z = 1

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:

Solve a quadratic equation by completing the square: leading coefficient 1

X.3Factor out a monomial

Lesson: Completing the square

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