Can someone help with this equation?

Question

√x+7 + 5 = x

a) {9}
b) {2,9}
c) {9,18}
d) {2}

Answer 1

√(x + 7) + 5 = x

Subtract 5 from both sides.

√(x + 7) = x - 5

Square both sides.

x + 7 = x^2 - 10x + 25

Combine like terms.

x^2 - 11x + 18 = 0

Factor.

(x - 9)(x - 2) = 0
x - 9 = 0 or x - 2 = 0
x = 2 or x = 9

However, when you check the answers, x = 2 is not a solution because the square root function does not return the negative value of square root; this data was lost when we squared both sides, and we can only regain it by checking the results. So x = 9 is the only solution, and the answer is choice a).

Answer 2

The correct answer is A.) 9.

To prove this, I am assuming that the formula is: Sqrt(x+7) + 5 = x

You simply then have to plug in the values from each answer independantly and see if x is equal on both sides.

Answer A: Sqrt(9+7) + 5 = 9
Sqrt(16) + 5 = 9
4+5 = 9
9=9

Answer B: Sqrt(2+7) + 5 = 2
Sqrt(9) + 5 = 2
3+5 = 2
8 = 2 No good
We already know 9 checks out by itself so no need to retest it.

Answer C: Sqrt(18+7) + 5 = 18
Sqrt(25) + 5 = 18
5 + 5 = 18
10 = 18 No good

Answer D: We already have shown in Answer B that 2 does not work.

Ergo, A is the only logical functioning answer.

Regards

Answer 3

sqrt(x + 7) + 5 = x

sqrt(x + 7) = x - 5 (power 2 both sides)

x + 7 = (x - 5 )^2

(x - 5)^ 2 = x + 7

x^2 - 10x +25 -x -7 = 0

x^2 -11x +8 = 0

( x -9) (x - 2) = 0

=> x - 9 = 0
x = 9

=> x - 2 = 0
x = 2

verification:

Nota:
Always verify the solutions to make sure all of them are ok.

x = 2 => sqrt(2 + 7) + 5 = 2
=> 3 + 5 = 2 (false)

x= 9 => sqrt(9 + 7) + 5 = 9
=> 4 + 5 = 9 (true)

Final answer : a) «9»

Answer 4

Question should read:-
√(x + 7) + 5 = x
√(x + 7) = x - 5
x + 7 = (x - 5)²
x + 7 = x² - 10x + 25
x² - 11x + 18 = 0
(x - 9) (x - 2) = 0
x = 2 , x = 9
ANSWER b)

Answer 5

You can just plug in the potential answers and see if they fit:

√x+7 + 5 = x
√(9+7) + 5 =? 9
√(16) + 5 =? 9
9 = 9

the others don't.

(a)

Answer 6

sqrt(x+7)=x-5
x+7=x^2-10x+25
x^2-11x+18=0
(x-2)(x-9)=0
x=2,9