example,
Solve by completing the square.
i. 3x^{2} = 9x
ii. 2x^{2} + 3x + 1 = 0
Solutions
i. 3x^{2} = 9x or
(3x^{2} - 9x = 0)
x^{2} - 3x = 0 (Step 1)
x^{2} - 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) 2x^{2} + 3x + 1 = 0 or (2x^{2} + 3x = -1)
X^{2} + (3x/2) = -(1/2) (step 1)
X^{2} + (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