Solve the following equation for x: x^2 - 4x - 17 = 4

First, take 4 from both sides of the equation to get everything on the LHS:x^2 - 4x - 17 - 4 = 4 - 4 so we have x^2 - 4x - 21 = 0We are looking to factorise the equation in the following way:(x + a)(x + b) = 0.To do this, we want a*b=-21 and a+b=-4Try a few factors of 21. We can see that (-3)7 = 21, but 7-3 = 4.Try 3(-7) = -21, now 3-7=-4, so(x + 3)(x - 7) = 0.For a product of two numbers to be 0, at least one of them must be zero, so we know that x + 3 = 0 or x - 7 = 0.In either case we move the numbers over to the RHS to get x = -3 or x = 7