Question

Find the real or imaginary solutions of the equation by factoring. x^4-8x^2=-16

Answer 1

ANSWER
$x=2$ or $x=-2$
EXPLANATION

The given equation is
${x}^{4} - 8 {x}^{2} = - 16.$

We set everything equal to zero to obtain,

${x}^{4} - 8 {x}^{2} + 16 = 0$

We rewrite the leading term to obtain,

${( {x}^{2} )}^{2} - 8( {x}^{2}) + 16 = 0$

This has now become a quadratic equation in
${x}^{2}$


We split the middle term to get,

${( {x}^{2} )}^{2} - 4 {x}^{2}- 4x^2+ 16 = 0$



We factor to get,


${x}^{2} (x^2-4)-4( {x}^{2}-4) = 0$


We factor further to get,


$( {x}^{2} -4)(x^2-4)= 0$



This gives

$( x-2)(x+2)(x-2)(x+2)= 0$


$( x-2)^2(x+2)^2= 0$



$x=2$ or $x=-2$