Please see the attached pdf and provide the solutions to the attached questions. Thanks!1.
(1 pt) Solve the following quadratic equation using the
property:
x
2
=
a
if and only if
x
=
p
a
or
x
=

p
a
, for any real
number
a
.
12
x
2
=
49
Solutions (separate by commas):
x
=
2.
(1 pt) ²ind all real solutions of the equation
(
x

4
)
2

25
=
0.
real solutions =
(Note: If there is more than one
real solution, give a comma separated list (i.e.: 1,2).)
3.
(1 pt) Solve the quadratic equation
(
x
+
3
)
2

23
=
0 by
taking square roots. If there is more than one correct answer,
enter your answers as a comma separated list.
x
=
4.
(2 pts) This problem is about using the are model to com
plete the square. Use the ”Handout: Area Model”, which is
in this week’s module on Canvas, to understand how the area
model works.
You are given:
x
2
+
14
x
+
.
Usetheareamodelto findthetermtoaddthatletsthepolynomialbe factoredintoaper fectsquare
.
Then factor
.
A. ²ill in the area model table for this problem. ²illing in the
bottom right box is literally, ”completing the square”.
multiplication
x
2
B. Add the needed term and factor.
x
2
+
14
x
+
=(
)
2
5.
(2 pts) This problem is about using the area model to
complete the square. Use the ”Handout: Area Model”, which
is in this week’s module on Canvas, to understand how the area
model works.
You are given:
x
2
+
10
x
+
9. Use the area model to rewrite
this quadratic in standard form (i.e., in completed square form).
A. ²ill in the area model table for this problem. ²illing in the
bottom right box is literally, ”completing the square”.
We only show one copy of the area model below. However
multiplication
x
2
B. When we enter the parts of
x
2
+
10
x
+
9 into the area
model, all the blanks are Flled, except one. What number must
we add to complete the square?
C. When we complete the square, we add something to the ex
pression
x
2
+
10
x
+
9 that was not originally there. What must
we now add, so that we do not change the original expression?
D. Write the the expression
x
2
+
10
x
+
9 in completed square
form:
1
Answer