<s>[INST] Solve for $x$, $3\sqrt{x+13} = x+9$ Solve equation: $3\sqrt{x+13} = x+9$
I squared both sides and got $9 + x + 13 = x^2 + 18x + 81$
I then combined like terms $x^2 + 17x + 59 = 0$
I then used the quadratic equation $x= -\frac{17}2 \pm \sqrt{\left(-\frac{17}2\right)^2-59}$ 
However, the answer is 3 
 [/INST] 3 √x+13 = x + 9
Squaring both sides, we get
9 (x + 13) = x^2 + 81 + 18x
9x + 117 = x^2 + 81 + 18x
x^2 + 18x - 9x + 81 - 117 = 0
x^2 + 9x - 36 = 0
x^2 + 12x - 3x - 36 = 0
x(x + 12) - 3(x + 12) = 0
(x + 12)(x - 3) = 0
Therefore, x = -12 or 3
However, when the problem equation does not get satisfied when x is substituted by -12, but it gets satisfied when x is substituted by 3.
Therefore, 3 is the required solution or root of the equation.
Hope that you understood the answer. 
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