1.4
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School
University of California, Berkeley *
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Course
N54
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
Pages
3
Uploaded by BailiffBookElephant2276
Question and Solution Template
Learning Attribute(s) Included in Question
: 1.4.4 Use the method of completing the square to transform any quadratic equation in x
into an equation of the form (
x
−
p
)
2
=
q
that has the same solutions. Derive the
quadratic formula from this form.
Calculator Active?
No
Question
:
What is the missing constant term in the perfect square that starts with
x
2
+
8
x
?
A)
8
B)
4
C)
2
D)
16
Equation Upload
(Please write the text of the question along with the LaTeX Code):
What is the missing constant term in the perfect square that starts with
$x^2+8x$?
A) $8$
B) $4$
C) $2$
D) $16$
Correct answer: D On a scale of 1-10, how difficult would you estimate your question to be (1=easy, 10=extremely difficult):
5 i
Solution
:
Step 1
: Let b
be the missing constant term.
Assume x
2
+
8
x
+
b
is factored to be perfect square ¿
¿
For the expressions to be the same, 2
a
must be equal to 8
and a
2
must be equal to b
.
Equation Upload (Please write the text of the question along with the LaTeX Code):
\textbf{Step 1}: .Let $b$ be the missing constant term.
Assume $x^2+8x+b$ is factored to be perfect square $(x+a)^{2}$
$(x+a)^{2}=x^2+2ax+a^2$
For the expressions to be the same, $2a$ must be equal to $8$ and $a^2$ must be equal to $b$.
Step 2:
Solve for a
2
a
=
8
a
=
4
Put a
=
4
to find the value of b
b
=
4
2
b
=
16
So, the missing term is 16
Equation Upload (Please write the text of the question along with the LaTeX Code):
\textbf{Step 2}: Solve for $a$
$$2a=8$$
$$a=4$$
Put $a=4$ to find the value of $b$
$$b= 4^2$$
$$b=16$$
So, the missing term is $16$
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