Question

find the real solution(s) of the equation ( x^6 + 36 = 100 ).
( x = ) (\boldsymbol{8}) (\boldsymbol{\times}) and ( x = ) (\boldsymbol{-8}) (\boldsymbol{\times})

Explanation:

Step1: Isolate $x^6$ term

Subtract 36 from both sides.
$x^6 = 100 - 36$

Step2: Simplify right-hand side

Calculate the difference.
$x^6 = 64$

Step3: Rewrite 64 as a sixth power

Express 64 as $2^6$ and $(-2)^6$.
$x^6 = 2^6 = (-2)^6$

Step4: Solve for real $x$

Take sixth root of both sides (real roots only).
$x = \pm 2$

Answer:

$x=2$ and $x=-2$