First, subtract #color(red)(45)# from each side of the equation to isolate the radical term while keeping the equation balanced:
#-color(red)(45) + 45 - sqrt(10 - 2x^2) = -color(red)(45) + 25#
#0 - sqrt(10 - 2x^2) = -20#
#-sqrt(10 - 2x^2) = -20#
Next, square both sides of the equation to eliminate the radical while keeping the equation balanced:
#(-sqrt(10 - 2x^2))^2 = (-20)^2#
#10 - 2x^2 = 400#
Then, subtract #color(red)(10)# from each side of the equation to isolate the #x# term while keeping the equation balanced:
#-color(red)(10) + 10 - 2x^2 = -color(red)(10) + 400#
#0 - 2x^2 = 390#
#-2x^2 = 390#
Then, divide each side of the equation by #color(red)(-2)# to isolate #x^2# while keeping the equation balanced:
#(-2x^2)color(red)(-2) = 390/color(red)(-2)#
#(color(red)(cancel(color(black)(-2)))x^2)cancel(color(red)(-2)) = -195#
#x^2 = -195#
Because any number squared always produces a positive result, there is no solution for #x# which will result in a negative 195.
Or, the solution is the null or empty set: #{O/}#
