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.

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,

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

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

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

Final answer:

$x=6+i\sqrt{3},6-i\sqrt{3}$