Solve the equation by using the square root property.
-$$( 3 z - 18 ) ^ { 2 } + 59 = 14$$
A) $\{ 14 + 3 \sqrt { 5 } , - 14 + 3 \sqrt { 5 } \}$
B) $\{ 6 + i \sqrt { 5 } , 6 - i \sqrt { 5 } \}$
C) $\{ 3 \sqrt { 5 } + 14 \}$
D) $\{ 3 \sqrt { 5 } - 14 \}$

Question

Quizplus · Accepted Answer

First, simplify the equation: $(3z - 18)^2 + 59 = 14$. Subtract 59 from both sides to get $(3z - 18)^2 = -45$. Taking the square root of both sides gives $3z - 18 = \pm \sqrt{-45}$, which simplifies to $3z - 18 = \pm 3i\sqrt{5}$. Solving for $z$ gives $z = 6 \pm i\sqrt{5}$.

Solve the Equation by Using the Square Root Property (3z−18)2+59=14( 3 z - 18 ) ^ { 2 } + 59 = 14(3z−18)2+59=14

Solve the Equation by Using the Square Root Property $( 3 z - 18 ) ^ { 2 } + 59 = 14$