Question

identify all of the following solutions of square root of x plus 14 end root plus 2 equals x

the possible answers are
x = -6
x = 1
x = -6 and x = 1
None of the above

@StudyGurl14

Answer 1

\[\sqrt{x+14}+2=x\]
\[\sqrt{x+14}=x-2\]
\[x+14=(x-2)^2\]
\[x +14 = x^2-4x+4\]
\[0=x^2-5x-10\]

Take the answer choices and plug them in and solve. If they come out to a true statement, that one is answer. If none of the answer choices work, the answer is "None of the above"

Answer 2

I'll do the first one so you can see how to do it:
\[x^2-5x-10=0\]
\[(-6)^2-5(-6)-10=0\]
\[36 +30 -10=0\]
\[56\neq0\]
So -6 is not a solution. Thus, you can eliminate answer choices A and C

Answer 3

is it none of the above? @StudyGurl14

Answer 4

correct

Answer 5

great! I need help with a few more
the next one is

which of the following is a solution to 6 square root of x plus 1 equals 24

the possible answers are

x = 17
x = 15
x = 5
x = 3

Answer 6

If I help you with this one will you please fan me and write a testimony?

Answer 7

of course! you're helping me so much

Answer 8

Great thanks!

Answer 9

\[6\sqrt{x}+1=24\]
Or...
\[6\sqrt{x+1}=24\]

Answer 10

is it x=3?

Answer 11

Which equation is it?

Answer 12

oh sorry its the second one

Answer 13

Okay
\[6\sqrt{x+1}=24\]
\[\sqrt{x+1}=4\]
\[x+1=4^2\]

Can you do the rest yourself?

Answer 14

yes thank you!

Answer 15

anytime :)

Answer 16

okay two more and I promise ill leave you alone!

1. Simplify 9 fourth root of 10 end root plus 2 cubed root of 10 end root minus 6 fourth root 10 end root 6 cubed root of 10

the possible answers for this one are
3 fourth root of 10 end root 4 cubed root of 10
3 fourth root of 20 end root minus 4 cubed root of 20
negative square root of 10
negative square root of 20

Answer 17

\[9\sqrt[4]{10}+2\sqrt[3]{10}-6\sqrt[4]{10}+6\sqrt[3]{10} \]
Like this?

Answer 18

yes! exactly like that

Answer 19

Okay, just combine like terms. the fourth roots are like terms with each other, and the cube roots are like term each other
9 - 6 = 3 and...
2 + 6 = 8 so...
\[3\sqrt[4]{10}+8\sqrt[3]{10}\]

Answer 20

great thanks!

and the last one is Multiply open parentheses 2 plus 5 square root of 3 close parentheses open parentheses 7 minus square root of 3

and the possible answers are
14 plus 28 square root of 3
14 minus 5 square root 3
negative 1 plus 33 square root of 3
negative 1 plus 37 square root of 3

Answer 21

\[(2+5\sqrt{3})(7-\sqrt{3})\]
\[14-2\sqrt{3}+35\sqrt{3}-5(3)\]
\[14+33\sqrt{3}-15\]
\[-1+33\sqrt{3}\]

Answer 22

thank you so so so so much!

Answer 23

You're so so so so welcome :)