Question

completing the square
solve ( x^2 - 16x + 60 = -12 ) by completing the steps
first, subtract (\boldsymbol{60}) from each side of the equation
complete
next, add (\boldsymbol{64}) to each side of the equation to complete the square.
complete
now, write ( x^2 - 16x + 64 = -8 ) as (\boldsymbol{\text{dropdown}})
done
options:
( (x - 8)^2 = -16 )
( (x - 8)^2 = -8 )
( (x - 16)^2 = -16 )
( (x - 16)^2 = -8 )

Explanation:

Step1: Verify first step (subtract 60)

Original equation: $x^2 - 16x + 60 = -12$
Subtract 60 from both sides:
$x^2 - 16x + 60 - 60 = -12 - 60$
$x^2 - 16x = -72$

Step2: Verify second step (add 64)

To complete the square for $x^2 -16x$, take half of -16 ($\frac{-16}{2}=-8$), square it: $(-8)^2=64$. Add 64 to both sides:
$x^2 -16x +64 = -72 +64$
$x^2 -16x +64 = -8$

Step3: Rewrite as perfect square

The left side is $(x-8)^2$, so:
$(x-8)^2 = -8$

Answer:

$(x - 8)^2 = -8$