The equations and their solutions are:
x^2 = –100 has no real solutions, since the square of any real number is nonnegative and cannot be negative.
5x^2 = 1 has two real solutions, x = ±√(1/5), because we can solve for x by taking the square root of both sides.
6x^2 + 17 = 11 has one real solution, x = ±√(6/3) = ±√2, because we can simplify the equation and solve for x by taking the square root of both sides.
7(x^2 + 6) = 42 has one real solution, x = ±√(36/7) = ±2√(7/7), because we can simplify the equation and solve for x by taking the square root of both sides.