Question

Complete the square to transform the quadratic equation into the form (x – p)2 = q.

x2 - 12x - 5 = 7

A) (x - 36)2 = 9
C) (x - 36)2 = -9
D) (x - 6)2 = -48

Answer 1

Answer:

Step-by-step explanation:

To complete the square, begin by separating the x terms from the constants by moving the constants to the other side of the equals sign:

$x^2-12x=12$

Now we can complete the square.  Take half the linear term, square it, and add it to both sides.  Our linear term is 12.  Half of 12 is 6, and 6 squared is 36.  We add 36 to both sides:

$(x^2-12x+36)=12+36$

In the process of completing the square we created a perfect square binomial.  I will state that binomial along with simplifying the right side of the equation:

$(x-6)^2=48$

That's the form you need it in.  I have a feeling that the B choice you left out is the one you want!

Answer 2

Answer:

(x - 6)2 = 48

Simplify and reorder:

x2 - 12x - 5 = 7

-12x + x2 = 12

The x term is -12x. Take half of its coefficient (-6). Square and add 36 to both sides. Reorder and combine.

-12x + x2 + 36 = 12 + 36

x2 - 12x + 36 = 48

Factor a perfect square on the left side:

(x - 6)2 = 48