Question 204020
Ok, you are good up to:
{{{x = (8+-sqrt(124))/10}}} Now you factor the 124 under the radical into {{{sqrt(124) = sqrt(4*31)}}} and the purpose of this step is to see if the radicand (the quantity under the radical) has any factors that are perfect squares. In this case, there is a factor of 4 which is a perfect square and can be moved out from under the radical by taking its square root, since:{{{sqrt(4) = 2}}}, so we get the next step:
{{{x = (8+2*sqrt(31))/10}}} or {{{x = (8-2*sqrt(31))/10}}} Notice that we can factor out a 2 in the numerator and also in the denominator.
{{{x = (cross(2)(4+sqrt(31)))/cross(2)(5)}}} or {{{x = (cross(2)(4-sqrt(31)))/cross(2)(5)}}} Cancel the 2's to leave you with:
{{{highlight(x = (4+-sqrt(31))/5)}}}