Question

1. write two equivalent forms for the given equation $x^2 - 12x + 11 = 0$

$\square$=0 (factored form)
$(\square)^2=\square$
show your work

1. write two equivalent forms for the given equation $x^2 - 11x - 51 = 0$

$\square$=0 (factored form)
$\square$

Explanation:

Step1: Find factored form

Factor $x^2 -12x +11$: look for two numbers multiplying to 11 and adding to -12, which are -1 and -11. So it factors to $(x-1)(x-11)$.

Step2: Complete the square

Isolate constant term: $x^2 -12x = -11$. Add $(\frac{-12}{2})^2=36$ to both sides: $x^2 -12x +36 = -11 +36$. Left side is $(x-6)^2$, right side is 25.

Answer:

$(x-1)(x-11)=0$
$(x-6)^2=25$