Solve the equation by the square root property.
-$$( 5 x - 8 ) ^ { 2 } = 12$$
A) $\left\{ \frac { 8 - 2 \sqrt { 3 } } { 5 } , \frac { 8 + 2 \sqrt { 3 } } { 5 } \right\}$
B) $\{ - 2 \sqrt { 5 } , 2 \sqrt { 5 } \}$
C) $\left\{ \frac { - 8 - 2 \sqrt { 3 } } { 5 } , \frac { - 8 + 2 \sqrt { 3 } } { 5 } \right\}$
D) $\left\{ - \frac { 4 } { 5 } , 4 \right\}$

Question

Quizplus · Accepted Answer

First, take the square root of both sides of the equation: $\sqrt{(5x - 8)^2} = \sqrt{12}$, which simplifies to $5x - 8 = \pm \sqrt{12}$. Solving for $x$ gives $x = \frac{8 \pm 2\sqrt{3}}{5}$.

Solve the Equation by the Square Root Property (5x−8)2=12( 5 x - 8 ) ^ { 2 } = 12(5x−8)2=12

Solve the Equation by the Square Root Property $( 5 x - 8 ) ^ { 2 } = 12$