Solve the equation.
-$\sqrt { 3 x + 10 } = 5 - 2 x$
A) $\left\{ \frac { 3 } { 4 } , 5 \right\}$
B) $\{ 5 \}$
C) $\left\{ \frac { 5 } { 4 } , 9 \right\}$
D) $\left\{ \frac { 3 } { 4 } \right\}$

Question

Quizplus · Accepted Answer

First, square both sides of the equation to eliminate the square root: $3x + 10 = (5 - 2x)^2$. Expanding the right side gives $3x + 10 = 25 - 20x + 4x^2$. Rearranging the equation to set it to 0 yields $4x^2 - 23x + 15 = 0$. Factoring or using the quadratic formula, we find that $x = \frac{3}{4}$ or $x = 5$. However, substituting $x = 5$ back into the original equation shows it does not satisfy the equation (as it results in a negative square root), leaving $x = \frac{3}{4}$ as the only solution.

Solve the Equation 3x+10=5−2x\sqrt { 3 x + 10 } = 5 - 2 x3x+10​=5−2x

Solve the Equation $\sqrt { 3 x + 10 } = 5 - 2 x$