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Find all solutions to the equation $\sqrt{3x+6}=x+2$. If there are multiple solutions, order them from least to greatest, separated by comma(s).

Aug 17, 2017

#1
+22188
+1

Find all solutions to the equation \sqrt{3x+6}=x+2 ($$\sqrt{3x+6}=x+2$$).
If there are multiple solutions,
order them from least to greatest, separated by comma(s).

$$\begin{array}{|rcll|} \hline \sqrt{3x+6} &=& x+2 \quad & | \quad \text{square both sides} \\ 3x+6 &=& (x+2)^2 \\ 3x+6 &=& x^2+4x+4 \\ x^2 +x -2 &=& 0 \\ (x+2)(x-1) &=& 0 \\\\ x_1 &=& -2 \\ x_2 &=& 1 \\ \hline \end{array}$$

Solution Set: {-2,1}

Proof:
$$x=-2:\qquad \sqrt{3\cdot(-2)+6} = -2+2\quad \checkmark \\ x=1: \qquad \sqrt{3\cdot(1)+6} = 1+2 \quad \checkmark$$

Aug 17, 2017

#1
+22188
+1

Find all solutions to the equation \sqrt{3x+6}=x+2 ($$\sqrt{3x+6}=x+2$$).
If there are multiple solutions,
order them from least to greatest, separated by comma(s).

$$\begin{array}{|rcll|} \hline \sqrt{3x+6} &=& x+2 \quad & | \quad \text{square both sides} \\ 3x+6 &=& (x+2)^2 \\ 3x+6 &=& x^2+4x+4 \\ x^2 +x -2 &=& 0 \\ (x+2)(x-1) &=& 0 \\\\ x_1 &=& -2 \\ x_2 &=& 1 \\ \hline \end{array}$$

Solution Set: {-2,1}

Proof:
$$x=-2:\qquad \sqrt{3\cdot(-2)+6} = -2+2\quad \checkmark \\ x=1: \qquad \sqrt{3\cdot(1)+6} = 1+2 \quad \checkmark$$

heureka Aug 17, 2017