Question

Solve the equation by completing the square. 1) X^2 - 6x + 10 = 0

Answer 1

The given equation is

$x^2-6x+10=0$

First, we subtract 10 from each side

$\begin{gathered} x^2-6x+10-10=-10 \\ x^2-6x=-10 \end{gathered}$

Then, we divide the linear coefficient by half and elevated it to the square power.

$(\frac{6}{2})^2=3^2=9$

Then, we add 9 on each side.

$\begin{gathered} x^2-6x+9=-10+9 \\ \end{gathered}$

Now, we factor the trinomial.

$(x-3)^2=-1$

At this point, we can deduct that the equation has no real solutions because there's no real number whose square power ends up in a negative number.

Hence, the equation has no solutions.