Question

Solve for x. (x - 4)(x - 4) = 0 a.-16 b. -4 c. 4 d. 16

Answer 1

7

Explanation:

x - 4 =

16 - x

(x - 4)2 = 16 - x

x2 - 8x + 16 = 16 - x

-x2 + 7x = 0

-(x(x - 7)) = 0

multiple both sides by -1:

x(x - 7) = 0

x = 0 or x = 7

Check solutions:

x = 7 ⇒

7 - 4 =

16 - 7

3 =

9

3 = 3

x = 7 is a solution

x = 0 ⇒

0 - 4 =

16 - 0

-4 =

16

-4 ≠ 4

x = 0 is not a solution (extraneous root)

Answer 2

(x - 4)(x - 4)=0. Then, (x - 4)=0 and (x - 4) =0.

In both cases, x is 4. Thus, you have a double real root: {4, 4}.