In parallelogram abcd , diagonals ac⎯⎯⎯⎯⎯ and bd⎯⎯⎯⎯⎯ intersect at point e, be=x2−21 , and de=4x . what is bd ? enter your answer in the box. [_] units

bearing in mind that in a parallelogram, both diagonals bisect each other, namely they cut each other in two equal halves, thus BE = DE.  Check the picture below.

we can't use x = -3, because for DE that'd give use a 4(-3) = -12, which doesn't work for a segment with a length greater than 0.

well, since DE = 4(7) = BE, that means BD = DE + BE = 28 + 28 = 56.