Question

What are the solutions to the equation x² = 256?

Select each correct answer.

(options)

−128

−16

16

128

Answer 1

the answer will be 16 and -16

Answer 2

ANSWER


`x = - 16 \: or \: x = 16`


Step-by-step explanation

We can use two different methods to solve this question.

Method 1: Square Root Method


We have,


`{x}^(2) = 256`


We take the plus or minus square root of both sides to obtain,


`x = \pm √(256)`



This implies that;


`x = \pm16`

We split the plus or minus sign to obtain,


`x = - 16 \: or \: x = 16`



Method 2: Factorization Method



`{x}^(2) = 256`


We equate everything to zero.


`{x}^(2) - 256 = 0`



`{x }^(2) - {16}^(2) = 0`


We apply difference of two squares



`(x - 16)(x + 16) = 0`



`x + 16 = 0 \: or \: x - 16 = 0`




`x = - 16 \: or \: x = 16`