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.

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\\√(D)=√(-20) \\√(D)=√(-1*4*5) \\ √(D)=2*√(-1*5)\\ √(-1)=i\\ √(D)=2i√(5) \\ x_(1,2)=(-bб√(D) )/(2) \\x_(1,2)=(-(-10)б2i√(5) )/(2)\\ x_(1,2)=(10б2i√(5) )/(2)\\ x_(1,2)=5бi√(5).`