Explanation:
this just means by solving an equation.
and that is simple to find.
as the diagonals of a parallelogram intersect each other at their midpoints, it means that both parts of the diagonal must be of equal length.
so,
x² + 9x = 4x + 6
x² + 5x - 6 = 0
the solution to a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (-5 ± sqrt(5² - 4×1×-6))/(2×1) =
= (-5 ± sqrt(25 + 24))/2 =
= (-5 ± sqrt(49))/2 = (-5 ± 7)/2
x1 = (-5 + 7)/2 = 2/2 = 1
x2 = (-5 - 7)/2 = -12/2 = -6
x2 would make QE and SE negative so that did not make any sense.
that leaves us with x1 (x = 1) as valid solution.
QE = x² + 9x = 1² + 9×1 = 1 + 9 = 10