Jack

example,

Solve by completing the square.

i. 3x² = 9x

ii. 2x² + 3x + 1 = 0      

Solutions

i. 3x² = 9x     or

(3x²  - 9x = 0)

x²  - 3x = 0       (Step 1)

 x² - 3x + (-(3/2)²) = -(3/2)²     (Step 2)

 x(-(3/2)²)= 9/4            (Step 3)           

x -3 = + √(9/4) (step 4)

(∴ x = (3/2) + (3/2))

= (3+3)/2 or (3/2) - (3/2) =

(= 3 or 0)

ii) 2x² + 3x + 1 = 0       or         (2x² + 3x = -1)

X² + (3x/2) = -(1/2)  (step 1)

X² + (3x/2) + (3/4)² = (3/4)² - 1/2     (step 2)

(x +(3/4)²) = 1/16 (step 3)

X + (3/4) = +  √(1/16)

X = - (3/4) = + (1/4)

-(3/4) + (1/4) or -(3/4)-(1/4)

X = -(1/2) or x = -1