Question

square root of the quantity x minus 2 end quantity plus 8 equals x

solve for x

Answer 1

Answer:

x = 11.

Step-by-step explanation:

√(x - 2) + 8 = x

√(x - 2) = x - 8

Square both sides:

x - 2 = (x - 8)^2

x - 2 =  x^2 - 16x + 64

x^2 - 17x + 66 = 0

(x - 6)(x - 11) = 0

x = 6, 11.

With this type of question we could have extraneous roots so:

Check these 2 roots:

x = 6:

√(2 - 6) + 8 = √(-4)+8   <----- has no real value so this is not a root,

x = 11:

√(11-2) + 8 = 11    <  ----Checks out.

Answer 2

Answer:

• x = {6, 11}

Step-by-step explanation:

• $\sqrt{x-2} + 8=x$
• $\sqrt{x-2} = x - 8$
• x - 2 = (x - 8)²
• x² - 16x + 64 = x - 2
• x² - 17x + 66 = 0
• x = (17 ± $\sqrt{17^2- 4*66}$) / 2
• x = (17 ± 5)/2
• x = 11
• x = 6