Question 923715
{{{x^2 -144 = 0}}}

{{{x^2 -12^2 = 0}}}

{{{(x-12)(x+12) = 0}}}

solutions:

if {{{(x-12)= 0}}}=> {{{highlight(x=12)}}}

if {{{(x+12)= 0}}}=> {{{highlight(x=-12)}}}



{{{x^4 -81 = 0}}}

{{{x^4 -3^4 = 0}}}

{{{(x^2)^2 -(3^2)^2 = 0}}}

{{{(x^2)-(3^2)(x^2)+(3^2) = 0}}}

{{{(x-3)(x +3)(x-3i)(x+3i) = 0}}}

solutions:
real:
if {{{(x-3) = 0}}}=> {{{highlight(x=3)}}}
if {{{(x+3)= 0}}}=>{{{highlight(x=-3)}}}
complex:
if {{{(x-3i)= 0}}}=>{{{highlight(x=3i)}}}
if {{{(x+3i)= 0}}}=>{{{highlight(x=-3i)}}}



{{{x^3 -27 = 0}}}

{{{x^3 -3^3 = 0}}}
{{{(x-3)(x^2+3x+9) = 0}}}

one solution: {{{(x-3)=0}}}=>{{{highlight(x=3)}}}

for {{{ (x^2+3x+9) = 0}}} use quadratic formula:

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 

{{{x = (-3 +- sqrt( 3^2-4*1*9 ))/(2*1) }}} 

{{{x = (-3 +- sqrt( 9-36 ))/2 }}}

{{{x = (-3 +- sqrt( -25 ))/2 }}}

{{{x = (-3 +- 5i)/2 }}}

complex solutions:

{{{x = (-3 + 5i)/2 }}}

{{{highlight(x = -3/2 + 5i/2 )}}}

and
{{{x = (-3 - 5i)/2 }}}

{{{highlight(x = -3/2 - 5i/2) }}}





{{{z^3 + 8 = 0}}}

{{{z^3 + 2^3 = 0}}}

{{{(z+2) (z^2-2z+4) = 0}}}


one solution: {{{(x+2)=0}}}=>{{{highlight(x=-2)}}}
for {{{ (z^2-2z+4)= 0}}} use quadratic formula:

{{{z = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 

{{{z= (-(-2) +- sqrt( (-2)^2-4*1*4 ))/(2*1) }}} 

{{{z = (2 +- sqrt(4-16 ))/2 }}}

{{{z = (2 +- sqrt( -12 ))/2 }}}

{{{z = (2 +- sqrt( -4*3 ))/2 }}}

{{{z = (2 +- 2i*sqrt(3))/2 }}}

complex solutions:

{{{x = (2 + 2i*sqrt(3))/2 }}}

{{{x = 2/2 + 2i*sqrt(3)/2 }}}

{{{highlight(x = 1+ sqrt(3)*i) }}}

and
{{{x = (2 -2i*sqrt(3))/2 }}}

{{{x = 2/2 - 2i*sqrt(3)/2 }}}

{{{highlight(x = 1- sqrt(3)*i) }}}