Question

What is the solution to the equation below. square root x - 6 = x - 12

Answer 1

`\\ \rm\hookrightarrow √(x-6)=x-12`

`\\ \rm\hookrightarrow x-6=(x-12)^2`

`\\ \rm\hookrightarrow x-6=x^2-24x+144`

`\\ \rm\hookrightarrow x^2-25x+150=0`

`\\ \rm\hookrightarrow x^2-10x-15x+150=0`

`\\ \rm\hookrightarrow (x-10)(x-15)=0`

`\\ \rm\hookrightarrow x=15\:or \:10`

Answer 2

`x = 15,10` || C and D is the correct choices.

Explanation:

`√(x-6)=x-12`

`x-6 =(x-12)^2`

`x-6 = x^2 -24x +144`

`x^2 -24x -x +144 +6 = 0`

`x^2 - 25x + 150= 0`

`x^2 -15x -10x +150=0`

`x(x-15)-10(x-15)=0`

`(x-15)(x-10) = 0`

`x = 15,10`