Homework help, no need to explain answer

He failed to check for extraneous solutions

Step-by-step explanation:

sqrt(x+6) -4 =x

Add 4 to each side

sqrt(x+6) -4+4 =x+4

sqrt(x+6)  =x+4

Sqaure each side

(sqrt(x+6))^2  =(x+4)^2

x+6 = x^2 +8x+16

Subtract 6 from each side

x = x^2 +8x +10

Subtract x from each side

0 = x^2 +7x +10

Factor

0 = (x+5) (x+2)

Using the zero product property

x=-5  x=-2

Check the solutions

sqrt(-5+6) -4 =-5

sqrt(1) -4 = -5

1-4 =-5

-3 does not equal -5 not a solution

sqrt(-2+6) -4 =-2

sqrt(4) -4 = -2

2-4 =-2  is a solution

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answer: d.) the total number of protons and neutrons is 15

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