Question

What are the solutions to the equation x² = 256?

Answer 1

The answer will be 16 and -16

Answer 2

ANSWER

$x = - 16 \: or \: x = 16$


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,

$x = \pm \sqrt{256}$



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


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


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



$x = - 16 \: or \: x = 16$