Question 51197
First, divide both sides by -9 to yield {{{ (-9(x-3)^2) / -9 = -7 / -9 }}}.  This simplifies to {{{ (x-3)^2 = 7/9 }}}.  Now take the square root of both sides to produce {{{ x-3 = sqrt(7/9) }}}.  Adding 3 to both sides produces {{{ x-3+3 = sqrt(7/9)+3 }}}, which simplifies to {{{ x = sqrt(7/9)+3 }}}.  {{{ sqrt(7/9) }}} is the same as {{{ sqrt(7)/sqrt(9) }}}, which simplifies to {{{ 2.64575 / 3 }}}, so now we have {{{ x = 2.64575/3 + 3 }}}, or {{{ x = 3.8819166 }}}.  To check our answer, substitute it into the original equation thusly:  {{{ -9(3.8819166-3)^2=-7 }}}.  This simplifies to {{{ -9*(.8819166)^2 = -7 }}}, which simplifies further to {{{ -9 * .77777688 = -7 }}}, which produces {{{ -6.9999919 = -7 }}}.  Because these number are extremely close, it means our answer of x = .8819166 is correct.