Question

solve the quadratic equation by completing the square.

$x^{2}-2x - 6=0$

the solution set is
(type an exact answer, using radicals as needed. use a comma to separate answers as needed)

Explanation:

Step1: Move the constant term.

$x^{2}-2x = 6$

Step2: Complete the square on the left - hand side.

The coefficient of $x$ is $-2$. Half of it is $-1$, and its square is $1$. Add $1$ to both sides of the equation: $x^{2}-2x + 1=6 + 1$.

Step3: Rewrite the left - hand side as a perfect square.

$(x - 1)^{2}=7$

Step4: Take the square root of both sides.

$x-1=\pm\sqrt{7}$

Step5: Solve for $x$.

$x = 1\pm\sqrt{7}$

Answer:

$1+\sqrt{7},1 - \sqrt{7}$