Verified answer

x + 4 = 4(the square root of)(x + 1)

(x + 4)/4 = (the square root of) (x + 1)

[(x + 4)/4]^2 = x + 1

(x^2 + 16)/16 = x + 1

x^2 + 16 = 16x + 16

x^2 - 16x = 0

x^2 - 16x - (16/2)^2 = (16/2)^2

x^2 - 16x + 256/4 = 256/4

x^2 - 16x + 64 = 64

(x - 8)^2 = 64

x - 8 = plus or minus 8

x = 16,0

Square both sides to cancel off the square root:

(x + 4) (x + 4) = 16(x + 1)

Expand all brackets:

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

Move everything to one side:

x^2 - 8x = 0

Factor out x:

x(x - 8) = 0

For your first solution divide both sides by (x - 8):

x = 0

For your second solution divide both sides by x:

x - 8 = 0

x = 8

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Overall:

x = 0, 8