Question

what is the intermediate step in the form $(x + a)^2=b$ as a result of completing the square for the following equation?
$x^{2}-8x - 9=-9$
answer attempt 1 out of 2
$(\square)^2 = \square$

Explanation:

Step1: Move the constant term

Add 9 to both sides of the equation $x^{2}-8x - 9=-9$, we get $x^{2}-8x=0$.

Step2: Complete the square

For the quadratic expression $x^{2}-8x$, the coefficient of $x$ is - 8. Half of it is $\frac{-8}{2}=-4$, and its square is 16. Add 16 to both sides of the equation $x^{2}-8x = 0$. So we have $x^{2}-8x + 16=16$.

Step3: Rewrite in square - form

The left - hand side $x^{2}-8x + 16$ can be written as $(x - 4)^{2}$ according to the perfect - square formula $(a - b)^2=a^{2}-2ab + b^{2}$ (here $a = x$ and $b = 4$). So we get $(x - 4)^{2}=16$.

Answer:

$(x - 4)^{2}=16$