Answer:
both
Step-by-step explanation:
When would these strategies work?
Esma wants to solve by completing the square. If our equation looks like
a
x
2
+
b
x
+
c
=
k
ax
2
+bx+c=ka, x, squared, plus, b, x, plus, c, equals, k, this strategy would work. If
a
=
1
a=1a, equals, 1, we can square half of
b
bb to find what number completes the square. If
a
>
1
a>1a, is greater than, 1, we need to factor before we complete the square.
Hunter wants to solve using the zero product property. If we have a factored expression that equals zero, this strategy would work.
Whose strategy would work to solve
x
2
+
8
x
=
2
x
−
8
x
2
+8x=2x−8x, squared, plus, 8, x, equals, 2, x, minus, 8?
Hint #22 / 4
Esma's strategy
Esma is correct that adding
1
11 to both sides completes the square. She can factor
x
2
+
6
x
+
9
x
2
+6x+9x, squared, plus, 6, x, plus, 9 and rewrite the equation as
(
x
+
3
)
2
=
1
(x+3)
2
=1left parenthesis, x, plus, 3, right parenthesis, squared, equals, 1. Then she can solve using square roots.
So Esma's strategy would work.
[Show me this strategy worked out.]
Hint #33 / 4
Hunter's strategy
Hunter is correct that he can factor
x
2
+
6
x
+
8
x
2
+6x+8x, squared, plus, 6, x, plus, 8 as
(
x
+
2
)
(
x
+
4
)
(x+2)(x+4)left parenthesis, x, plus, 2, right parenthesis, left parenthesis, x, plus, 4, right parenthesis.
He can then solve
(
x
+
2
)
(
x
+
4
)
=
0
(x+2)(x+4)=0left parenthesis, x, plus, 2, right parenthesis, left parenthesis, x, plus, 4, right parenthesis, equals, 0 using the zero product property since he has a factored expression equal to zero.
So Hunter's strategy would work.
[Show me this strategy worked out.]
Hint #44 / 4
Answer
Both of Esma's and Hunter's strategies would work.
first. By doing this, it would then give us our answer as 16. By us understanding this point of view, we would then consider that this would then be your answer. That would then include that there would then be 16 pairs of the "enantiomeric pairs", and that would then be the possible estimate.