Question

4.7/4.8 et - complete the square
possible points: 15
solve the problem shown below by completing the square. when you are finished, please take a picture of your work and upload here.
$x^2 - 6x + 3 = 0$

Explanation:

Step1: Isolate the x-terms

Subtract 3 from both sides of the equation $x^2 - 6x + 3 = 0$ to get $x^2 - 6x = -3$.

Step2: Complete the square

Take half of the coefficient of x, which is $\frac{-6}{2} = -3$, square it: $(-3)^2 = 9$. Add this to both sides: $x^2 - 6x + 9 = -3 + 9$.

Step3: Factor the left side

The left side is a perfect square trinomial, so it factors to $(x - 3)^2 = 6$.

Step4: Solve for x

Take the square root of both sides: $x - 3 = \pm\sqrt{6}$. Then add 3 to both sides: $x = 3 \pm\sqrt{6}$.

Answer:

$x = 3 + \sqrt{6}$ or $x = 3 - \sqrt{6}$