Question

Please help!

Use the method of completing the square to

Transform the quadratic equation into the equation form (x _ p)2 = q.

-9 + 12x - 6x^2 = 0


A)
(x - 1)2 = -0.5
B)
(x - 1)2 = -1.5
C)
(x - 1)2 = 0.5
D)
(x - 1)2 = 1.5

Answer 1

The answer is C) (x - 1)2 = 0.5

The equation is
-9 + 12x - 6x² = 0
Multiply the following equation by (-1) on the both sides:
9 - 12x + 6x² =0

Now, we will use the method of completing the square:
ax² + bx + c = 0 ⇒ a(x + d)² + e = 0,
where d = b/2a, e = c - b² / 4a

The quadratic equation is: ax² + bx + c = 0
Our equation is: 6x² - 12x + 9 = 0
so in our equation a = 6, b = -12, c = 9

Now, let's replace it:
d = b/2a = -12/2*6 = -12/12 = -2
e = c - b² / 4a = 9 - (-12)²/4*6 = 9 - 144/24 = 9 - 6 = 3
a(x + d)² + e = 0,
6(x + (-1))² + 3 = 0
6(x - 1)² = 3
(x - 1)² = 3/6
(x - 1)² = 1/2
(x - 1)² = 0.5