You know from the geometry of the problem that
.. 7^2 = y*(y +11)
.. 49 = y^2 +11y
.. y^2 +11y -49 = 0 . . . . . . . . the quadratic equation in standard form
Now, you're ready to use the quadratic formula. You have
.. a = 1
.. b = 11
.. c = -49
.. y = (-b ±√(b^2 -4ac))/(2a)
.. y = (-11 ±√(11^2 -4*1*(-49)))/(2*1) . . . . . substitute the values for a, b, c
.. = (-11 ±√317)/2 ≈ {-14.4, 3.4}
Since segment lengths can only be positive,
.. y ≈ 3.4 cm
