How to get complex numbers as an answer in an equation?

Question

Write a check to show that 2+5i and 2-5i are the two solutions to the equation x^2-3x+30 = x+1.

Answer 1

x^2 - 3x + 30 = x + 1
x^2 - 4x + 29 = 0
a = 1, b = -4, c = 29
quadratic formula is: x = (-b + or - (b^2 - 4ac)^1/2) / 2a
x = (4 + or - (16 - 116)^1/2) / 2
x = (4 + or - (-100)^1/2) / 2
square root of -100 is 10i...
x = (4 + or - 10i) / 2
x = 2 + 5i or 2 - 5i

Answer 2

first bring x+1 to the other side of the equasion so that x^2-4x+29=0.then use the quadratic formula: x= (4 + or - the square root of 16-4*29)/2. because 4*29=116 and 16-116 is -100, the square root of a negative number must contain i. the square root of -100 is 10i or -10i. after doing the quadratic formula, you should get 4 + or - 10i/2. both 4 and 10 are divisible by two, so the answer you get is 4+5i, 4-5i.