1. Solve each equation, if possible. Write irrational numbers in simplest radical form. Describe the strategy you used to get your solution and tell why you chose that strategy.
x^2 + 4 = 0 Using the square root method, subtract 4 from both sides. x^2 = -4 To clear the power of 2, take the square root of both sides. x = + - square rot of (-4) x = + - 2i This is a complex answer because the radicand was a negative number.
x^2 - 6x + 1 = 0 I would use completing the square to solve this problem. Subtract 1 from both sides. x^2 - 6x = -1 When completing the square, take the b term (-6) and divide by 2 (-6/2= -3), then square this number (9), add the number to both sides. x^2 - 6x + 9 = -1 + 9 The left side is now a perfect square trinomial. (x - 3)^2 = 8 To clear the power of 2, take the square root of both sides. x - 3 = + - sqrt 8 add 3 to both sides and simplify sqrt 8 x = 3 + - 2sqrt2
