The square root of 2x + 1 can be written as (2x + 1)

(x - 7)

x

x

factor

(x - 12)(x - 4) = 0

set each to 0 to determine the solution set

x - 12 = 0 x - 4 = 0

x = 12 x = 4

the answer is 4 and 12

the reason 4 works is because (2(4) + 1)

so 4 = 7 + (-3)

4 = 4

^{1/2}x = 7 + (2x + 1)^{1/2}square both sides(x - 7)

^{2}= ((2x + 1)^{1/2})^{ 2}x^{2 }-14x + 49 = 2x + 1x

^{2}-14x + 49 - 2x - 1 = 0x

^{2}- 16x + 48 = 0factor

(x - 12)(x - 4) = 0

set each to 0 to determine the solution set

x - 12 = 0 x - 4 = 0

x = 12 x = 4

the answer is 4 and 12

the reason 4 works is because (2(4) + 1)

^{1/2 }= 9^{1/2 }= + 3 or -3so 4 = 7 + (-3)

4 = 4