Solve.
-$$\sqrt { 3 x + 14 } = x + 3$$
A) 0
B) $\frac { - 3 \pm \sqrt { 29 } } { 2 }$
C) $\frac { - 3 + \sqrt { 29 } } { 2 }$
D) $\frac { - 3 - \sqrt { 29 } } { 2 }$

Question

Quizplus · Accepted Answer

To solve the equation $\sqrt{3x + 14} = x + 3$, first square both sides to eliminate the square root: $3x + 14 = (x + 3)^2$. Expanding the right side gives $3x + 14 = x^2 + 6x + 9$. Rearranging the equation to set it to 0 yields $x^2 + 3x - 5 = 0$. Using the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, with $a = 1$, $b = 3$, and $c = -5$, we find $x = \frac{-3 \pm \sqrt{29}}{2}$. However, only the positive root, $\frac{-3 + \sqrt{29}}{2}$, satisfies the original equation, making option C correct.

Solve - 3x+14=x+3\sqrt { 3 x + 14 } = x + 33x+14​=x+3

Solve
- $\sqrt { 3 x + 14 } = x + 3$