Esma and Hunter were trying to solve the equation: x2 + 8x = 2x - 8

They both agreed they should first subtract 2x and add 8 to both sides and rewrite the equation as

22 + 6x + 8 = 0.

Then Esma said, "I can complete the square. I can add 1 to both sides to rewrite this equation as

22 + 6x + 9 = 1, factor, and solve using square roots."

Hunter said, "I'll factor the left-hand side of the equation as (x + 2)(x + 4) and solve using the zero

product property."

Whose solution strategy would work?

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.

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752

a mantle plume is an upwelling of abnormally hot rock within the earth's mantle. as the heads of mantle plumes can partly melt when they reach shallow depths, they are thought to be the cause of volcanic centers known as hotspots and probably also to have caused flood basalts.

step-by-step explanation: