Question

question 10 of 10 which of the following are solutions to the equation below? check all that apply. (3x + 4)^2 = 14 a x = (-√14 - 4)/3 b x = (√14)/3 - 4 c x = - (√14)/3 - 4 d x = - (√10)/3 e x = (√14 - 4)/3 f x = (√10)/3

Explanation:

Step1: Take square - root of both sides

\[

$$\begin{align*} (3x + 4)^2&=14\\ 3x+4&=\pm\sqrt{14} \end{align*}$$

\]

Step2: Solve for \(x\) when \(3x + 4=\sqrt{14}\)

\[

$$\begin{align*} 3x&=\sqrt{14}- 4\\ x&=\frac{\sqrt{14}-4}{3} \end{align*}$$

\]

Step3: Solve for \(x\) when \(3x + 4=-\sqrt{14}\)

\[

$$\begin{align*} 3x&=-\sqrt{14}-4\\ x&=\frac{-\sqrt{14}-4}{3} \end{align*}$$

\]

Answer:

A. \(x=\frac{-\sqrt{14}-4}{3}\), E. \(x=\frac{\sqrt{14}-4}{3}\)