Question

-X² + 5x - 6 = 2
Using the quadratic formula

Answer 1

`-x^2+5x-6=2\\-x^2+5x-6-2=0\\-x^2+5x-8=0\\`

↝ Form into
`ax^2+bx+c = 0` where a > 0 (Optional)

`x^2-5x+8=0` ↝ Multiply -1 for both sides.

↝ Then proceed with the Quadratic Formula.

x = [-b ± (√b²-4ac)]/2a ↝ Quadratic Formula

`x=(-(-5)+-√((-5)^2-4(1)(8)))/(2(1))\\x=(5+-√(25-32))/(2)\\`

↝ As you can see that inside the square root, the numbers cannot be negative. Therefore, the solutions are imaginary.

↝ Solution with Real Numbers System ↝ There are no real solutions.

↝ Solution with Complex Number System ↝

`x=(5+-√(25-32))/(2)\\x=(5+-√(-7))/(2)\\x=(5+-√(7)i )/(2)`

Therefore, the answer for Complex Number System is (5±√7i)/2