Verified answer

You have to think :

How to eliminate the sq root...!

Write :

(sq root of x+3) = 2 - 3(x+3)

3(x+3) + (sq root of x+3) = 2

(sq root of x+3) = 2 - 3(x+3)

x + 3 = (2 - 3x - 9)^2

x + 3 = (-3x -7)^2

x + 3 = 9x^2 + 42x + 49

0 = 9x^2 + 41x + 46

Now use the quadratic equation to find x.

3x + 9 + sqrt(x+3) = 2

sqrt(x+3) = -3x - 7

x + 3 = (-3x - 7)²

x + 3 = 9x² + 42x + 49

9x² + 41x + 46 = 0

-41 +/- sqrt(41² - 4(9)(46))

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18

-41 +/- sqrt(25)

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18

(-41 +/- 5) / 18

x = -46/18 or -36/18 = -23/9 or -2