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