Answer:
[tex]\large\boxed{x=2,\ -2}[/tex]
Step-by-step explanation:
[tex]\text{If the trapezoid EFGH is isosceles, then the angles}\ HEF\ \text{and}\ GFE\\\\\text{are congruent. Therefore}\ m\angle HEF=m\angle GFE.\\\\\text{We have the equation}\\\\4x^2+16=5x^2+12\qquad\text{subtract 16 from both sides}\\\\4x^2=5x^2-4\qquad\text{subtract}\ 5x^2\ \text{from both sides}\\\\-x^2=-4\qquad\text{change the signs}\\\\x^2=4\to x=\pm\sqrt4\\\\x=-2\ or\ x=2[/tex]
