Question

completing the square.x² - 4x+1=0First, choose the appropriate form and fill in the blanks with the correct numbers.Then, solve the equation. If there is more than one solution, separate them with commas.

Answer 1

To complete the square, you need to add or substract a number that makes the expression become a perfect square trinomial.

In this case, it is necessary to add 3 to both sides of the expression, this way:

`\begin{gathered} x^2-4x+1+3=3 \\ x^2-4x+4=3 \end{gathered}`

Now, factor the expression:

`(x-2)^2=3`

(That is the appropiate form).

Now, solve the expression for x:

`\begin{gathered} (x-2)^2=3 \\ x-2=\sqrt[]{3} \\ x=\sqrt[]{3}+2 \end{gathered}`