Question 409320
You are perfect up to:
{{{y = (-4 +- sqrt (32))/8}}}
Next we simplify the square root. Square roots of perfect squares are fairly simple to simplify. 32 is not a perfect square so it is not as easy to simplify this square root. But 32 does have a perfect square factor:
{{{y = (-4 +- sqrt (16*2))/8}}}
Now we can use a property of radicals, {{{root(a, p*q) = root(a, p)*root(a, q)}}}, to split the square root into the product of the square roots of the factors:
{{{y = (-4 +- sqrt (16)*sqrt(2))/8}}}
The square root of the perfect square simplifies:
{{{y = (-4 +- 4*sqrt(2))/8}}}
Now we can reduce the fraction. Reducing fractions involves canceling common factors. So we need to factor the numerator and denominator:
{{{y = (4(-1 +- sqrt(2)))/(4*2)}}}
as you can see, there is a common factor we can cancel:
{{{y = (cross(4)(-1 +- sqrt(2)))/(cross(4)*2)}}}
leaving:
{{{y = (-1 +- sqrt(2))/2}}}
This is as far as we can go with the "+-". We can write this in "long form":
{{{y = (-1 + sqrt(2))/2}}} or {{{y = (-1 - sqrt(2))/2}}}