Here, the solutions are 2 plus or minus root 3, all divided by 2. Fantastic
work if you figured this one out. We begin to solve by moving this 8r term and
this negative 1 to the left-hand side of the equation. So we subtract 8r from
both sides, and then, we add positive 1 to both sides as well. Now that we have
our quadratic equation set equal to 0, we can use the values of a, b, and c
inside of our quadratic equation. a is equal to 4, b is equal to negative 8,
and c is equal to positive 1. We substitute these values using parenthesis
around each one. The negative of negative 8 is positive 8, negative 8 squared
is positive 64, and these three factors give us a product of negative 16. Here,
the denominator just simplifies to 8. We subtract inside our radical to get 8
plus or minus the square root of 48, all divided by 8. Next, we want to
simplify this radical by splitting it up into 16 times 3. The square root of 16
equals 4, and then we can factor a 4 from our numerator to get 4 times 2 plus
or minus 1 root 3. Since a factor of 4 appears in the numerator and in the
denominator, we simplify one last time to get 2 plus or minus 1 root 3, all
divided by 2. You might have also split this up into two separate fractions and
had 2 divided by 2 plus or minus root 3 divided by 2. Of course, this 2 divided
by 2 simply reduces to 1. So these would have also been acceptable answers, 1
plus or minus root 3 divided by 2.
