Question

Solve x2 + 2x + 9 = 0

a. X=-2 + or - 4i squareroot 2
b. x= -2 + or - 2i squareroot 2
c. x= -1 + or - 4i squareroot 2
d. x = -1 + or - 2i squareroot 2

Answer 1

`x^(2)+2x+9=0 \\ \\ x^(2)+2x+1+8=0 \\ \\ (x+1)^(2)+(2 √(2))^(2)=0 \\ \\ (x+1+2 √(2)i)(x+1-2 √(2)i)=0 \\ \\ x+1+2 √(2)i=0 \ \vee \ x+1-2 √(2)i=0 \\ \\ x=-1-2 √(2)i \ \vee \ x=-1+2 √(2)i`

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`a^(2)+b^(2)=(a+bi)(a-bi)`

Answer 2

`x^2+2x+9=0 \\ \\ a=1 \\ b=2 \\ c=9 \\ b^2-4ac=2^2-4 * 1 * 9=4-36=-32 \\ \\ x=(-b \pm √(b^2-4ac))/(2a)=(-2 \pm √(-32))/(2 * 1)=(-2 \pm √(-16 * 2))/(2)=(-2 \pm 4i√(2))/(2)=-1 \pm 2i√(2)`

The answer is D.