Solve the equation by the square root property.
-$$( x - 3 ) ^ { 2 } = - 6$$
A) $\{ 3 \pm \sqrt { 6 } \}$
B) $\{ - 3 \pm 6 \mathrm { i } \}$
C) $\{ - 3,9 \}$
D) $\{ 3 \pm i \sqrt { 6 } \}$

Question

Quizplus · Accepted Answer

The equation $(x - 3)^2 = -6$ suggests the use of the square root property, which leads to $x - 3 = \pm \sqrt{-6}$. Since $\sqrt{-6} = \sqrt{6}i$, the solution is $x = 3 \pm \sqrt{6}i$, which matches choice D.

Solve the Equation by the Square Root Property (x−3)2=−6( x - 3 ) ^ { 2 } = - 6(x−3)2=−6

Solve the Equation by the Square Root Property $( x - 3 ) ^ { 2 } = - 6$