Question

Solve the equation. x^2-12x+39=0

Answer 1

Given:

`x^2-12x+39=0`

Required:

We need to solve the given equation.

Step-by-step explanation:

Consider the given equation.

`x^2-12x+39=0`

which is of the form

`ax^2+bx+c=0`

where a=1, b=-12, and c=39.

Consider the quadratic formula,

`x=(-b\pm√(b^2-4ac))/(2a)`

Substitute a=1, b=-12, and c=39 in the formula.

`x=(-(-12)\pm√((-12)^2-4(1)(39)))/(2(1))`
`x=(12\pm√(144-156))/(2)`
`x=(12\pm√(-12))/(2)`
`Use\text{ \lparen-1\rparen=i}^2.`
`x=(12\pm√((2i)^23))/(2)`
`x=(12\pm2i√(3))/(2)`
`x=6\pm i√(3)`
`x=6+i√(3),6-i√(3)`

Final answer:

`x=6+i√(3),6-i√(3)`