square root of (3x+18) =x

Question

solve for x

Answer 1

√(3x + 18) = x

Square:

3x + 18 = x²

Subtract x2:

-x² + 3x + 18 = 0

Multiply both sides by -1:

x² - 3x - 18 = 0

So to factor we need m + n = -3 and mn = -18

-6 + 3 = -3

-6 * 3 = -18

(x - 6) (x + 3) = 0

x = 6 or -3

 

Note that since we used a squaring function, now more than ever we need to check our possibilities:

√(3 * -3 + 18) = -3

We can't get a negative when we root unless we use imaginary numbers, so that's out.

 

√(3 * 6 + 18) = 6

√(18 + 18) = 6

√36 = 6

6 = 6

So x = 6

Answer 2

√(3x + 18) = x

3x + 18 = x²         square both sides

0 = x²- 3x - 18      set equal to zero

0 = (x - 6)(x + 3)  FOIL

 

-3 is an extraneous root