Question

First, use the "completing the square" process to write this equation in the form (x + D)² = E. x² - 8 x + 12 = 0 is equivalent to:

Answer 1

D = -4

E = 2

Explanation:

The procedure for completing the square method is given as:

x2 + bx + c = 0

x2 + bx = -c

x2 + bx + (b/2)2 = -c + (b/2)2

Aolving the LHS simultaneously,

(x + b)2 = -c + (b/2)2

Find the square root of both sides,

(x + b) = sqrt(-c + (b/2)2)

So for the equation, x2 - 8x + 12

x2 - 8x = -12

x2 - 8x + 16 = -12 + 16

(x - 4)2 = 4

So square root both sides,

(x - 4) = 2

Comparing this to the equation given,

(x - D) = E;

D = -4

E = 2