Question

Solve x^2−6x+15=0 by completing the square

Answer 1

Completing the square is represented by:

`x^2+bx+((b)/(2))^2+c=d+((b)/(2))^2`

Then,

`\begin{gathered} x^2-6x+((-6)/(2))^2=d+(-(6)/(2))^2 \\ x^2-6x+9+15=0+9 \\ x^2-6x+24=9 \\ \end{gathered}`

By the rule of discriminant, we know that this expression has not real solutions.

`\text{Discriminant}=(b^2-4ac)`

If the discriminant is negative, the quadratic equation doesn't have real solutions.