Write x² + 4x -16 = 0 in the form (x+a)² - b = 0. Solve the equation giving your answer in surd form as simply as possible.
x² + 4x -16 = 0 (x+2)² -20 = 0 We note that the coefficient of x2 is 1 and the coefficient of x is 4. Therefore we say the that square is (x+2). This leaves us with an additional 4 from this expansion. We must therefore take away 4 from the left side. (x+2)² -16 -4 = 0 We then need to simplify this and move the constant to the right hand side. (x+2)² = 20 We want to solve for x not (x+2)2 so we need to square root both sides. x+2 = √20 20 is 4*5 or 22*5 so we can further simplify.x+2 = ±2√5 we want to get x on its own so we take 2 away from both sidesx = -2 ± 2√5
