How do you solve the quadratic equation #(3x - 9)^2 = 12# by the square root property?

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Answer 1 · 2015-08-31T23:35:35

#x = 3 +- (2sqrt(3))/3#

The square root property tells you that if #x^2# is equal to a positive number #n#, then you have

#color(blue)(x = +- sqrt(n))#

You can use #3# as a common factor to rewrite the expression that's being squared like this

#[3(x-3)]^2 = 3^2 * (x-3)^2 = 9 * (x-3)^2#

The equation can thus be written as

#(color(red)(cancel(color(black)(9))) * (x-3)^2)/color(red)(cancel(color(black)(9))) = 12/9#

#(x-3)^2 = 4/3#

The square root property tells you that

#x - 3 = +- sqrt(4/3)#

#x - 3 = +- 2/sqrt(3) = +- (2sqrt(3))/3#

This means that you get

#x = 3 +- (2sqrt(3))/3#

The two solutions to the equation will be

#x_1 = 3 + (2sqrt(3))/3" "# and #" "x_2 = 3 - (2sqrt(3))/3#