Solve the equation by using the Square Root Property. ( 2 x + 2 ) 2 = − 17 ( 2 x + 2 ) ^ { 2 } = - 17 ( 2 x + 2 ) 2 = − 17 A) x = ± 19 2 i x = \pm \sqrt { \frac { 19 } { 2 } } i x = ± 2 19 i B) x = − 2 ± 17 i 2 x = \frac { - 2 \pm \sqrt { 17 } i } { 2 } x = 2 − 2 ± 17 i C) x = ± 17 i 2 − 2 x = \pm \frac { \sqrt { 17 } i } { 2 } - 2 x = ± 2 17 i − 2 D) x = ± 2 + 17 i 2 x = \frac { \pm 2 + \sqrt { 17 } i } { 2 } x = 2 ± 2 + 17 i E) x = 2 ± 17 i x = 2 \pm \sqrt { 17 } i x = 2 ± 17 i

Question

Solve the equation by using the Square Root Property.   ( 2 x + 2 )  2 = − 17 ( 2 x + 2 )  ^ { 2 } = - 17 ( 2 x + 2 )  2 = − 17 A)    x = ± 19 2 i x = \pm \sqrt { \frac { 19 } { 2 } } i x = ± 2 19 ​ ​ i B)    x = − 2 ± 17 i 2 x = \frac { - 2 \pm \sqrt { 17 } i } { 2 } x = 2 − 2 ± 17 ​ i ​ C)    x = ± 17 i 2 − 2 x = \pm \frac { \sqrt { 17 } i } { 2 } - 2 x = ± 2 17 ​ i ​ − 2 D)    x = ± 2 + 17 i 2 x = \frac { \pm 2 + \sqrt { 17 } i } { 2 } x = 2 ± 2 + 17 ​ i ​ E)    x = 2 ± 17 i x = 2 \pm \sqrt { 17 } i x = 2 ± 17 ​ i

Danny Pacheco · Accepted Answer

Final Answer : B, Explanation :  Using the Square Root Property we have$(2x+2)^2=-17 2x+2=\pm\sqrt{-17}i 2x+2=\pm i\sqrt{17} 2x=-2\pm i\sqrt{17} x=\frac{-2\pm i\sqrt{17}}{2}  $$x=\boxed{\frac{-2\pm\sqrt{17}i}{2}}$

Solve the equation by using the Square Root Property. $2 x + 2 ) ^ { 2 } = - 17$

A) $\pm \sqrt { \frac { 19 } { 2 } } i$
B) $\frac { - 2 \pm \sqrt { 17 } i } { 2 }$
C) $\pm \frac { \sqrt { 17 } i } { 2 } - 2$
D) $\frac { \pm 2 + \sqrt { 17 } i } { 2 }$
E) $\pm \sqrt { 17 } i$

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