Question

Solve -3x² + 30x - 90 = 0. A.) x=5±2i√5 B.) x=5±i√5 C.) x=10±2i√5 D.) x= 10±i√5

Answer 1

Answer: B.) x=5±i√5.

Step-by-step explanation:

$\displaystyle\\-3x^2+30x-90=0\\-3*x^2-((-3)*10)*x+((-3)*30)=0\\-3*(x^2-10x+30=0\\Divide\ the\ equation\ by\ -3:$

$\displaystyle\\x^2-10x+30=0\\a=1\ \ \ \ b=-10\ \ \ \ c=30\\D=b^2-4ac\\D=(-10)^2-4*1*30\\D=100-120\\D=-20\\\sqrt{D}=\sqrt{-20} \\\sqrt{D}=\sqrt{-1*4*5} \\ \sqrt{D}=2*\sqrt{-1*5}\\ \sqrt{-1}=i\\ \sqrt{D}=2i\sqrt{5} \\ x_{1,2}=\frac{-bб\sqrt{D} }{2} \\x_{1,2}=\frac{-(-10)б2i\sqrt{5} }{2}\\ x_{1,2}=\frac{10б2i\sqrt{5} }{2}\\ x_{1,2}=5бi\sqrt{5}.$