Respuesta :
√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
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 with Step-by-step explanation:
we are given a equation
[tex]\sqrt{x+8}-6=x[/tex]
add 6 to both sides
[tex]\sqrt{x+8}=x+6[/tex]
squaring both sides
[tex]x+8=(x+6)^2[/tex]
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
