Looks ok, except that we do not multiply both sides by 4 for part a as the line in part a was given as an expression rather than as an equation (hence, there is only one side to talk about).

a)


x² + 11x - 15

= x² + 11x + (11/2)² - (11/2)² - 15

= (x + 11/2)² - 121/4 - 15

= (x + 11/2)² - 181/4


b)

When x² + 11x - 15 = 0,

(x + 11/2)² - 181/4 = 0

(x + 11/2)² = 181/4

(x + 11/2) = ±√181/4

x + 11/2 = √181/4 or x + 11/2 = -√181/4

x = √181/4 - 11/2 or x = -√181/4 - 11/2

x = (√181 - 11)/2 or x = -(√181 + 11)/2

x ≈ 1.23 or x ≈ -12.23

(2 d.p)


There is no need to x4, it doesn't make the equation easier to solve