Question

solve the equation by completing the square
x^2-6x+7=0

Answer 1

To complete the square, we need to add a constant term to both sides of the equation that will allow us to write the left side as a perfect square trinomial. We can determine this constant term by taking half of the coefficient of x, squaring it, and adding it to both sides.

- First, let's take half of the coefficient of x:

-6/2 = -3

- Now let's square it:

(-3)^2 = 9

- Finally, let's add 9 to both sides of the equation:

x^2 - 6x + 7 + 9 = 9

- Simplifying the left side:

(x - 3)^2 = 2

- Taking the square root of both sides:

x - 3 = ±√2

- Adding 3 to both sides:

x = 3 ± √2

The solution is x = 3 ± √2.