Question

Identify all of the following solutions of square root of x plus 8 end root minus 6 equals x.

a) x=-4
b) x=-7
c) x=-4 and x=-7
d) none of the above

Answer 1

√x+8 -6 = x
add 6 to both sides
√x+8 = x + 6
square both sides to get rid of the radical on the left side
(√x+8)² = (x+6)²
FOIL the (x+6)²
x+8 = x² + 12x +36
subtract x from the both sides
8 = x² + 11x + 36
subtract 8 from both sides
0 = x² + 11x + 28
7 times 4 is 28; 7+4=11
0 = (x+4)(x+7)
x = -7, -4
so the answer is C

Answer 2

Answer with Step-by-step explanation:

we are given a equation

`√(x+8)-6=x`

add 6 to both sides

`√(x+8)=x+6`

squaring both sides

`x+8=(x+6)^2`

x+8 = x² + 12x +36

subtract x from the both sides

8 = x² + 11x + 36

subtract 8 from both sides

0 = x² + 11x + 28

or x²+11x+28=0

splitting the middle term

x²+7x+4x+28=0

x(x+7)+4(x+7)=0

(x+4)(x+7)=0

x+4=0 or x+7=0

x= -4 or x= -7

Hence, Correct option is:

c) x= -4 and x= -7