Question

URGENT!!!

PLEASE HELP 30PTS
Complete the square to transform the quadratic equation into the form (x – p)2 = q. x2 - 8x - 10 = 18
A) (x - 8)2 = 14
B) (x - 4)2 = 44
C) (x - 8)2 = -14
D) (x - 4)2 = -44

Answer 1

B: (x - 4)² = 44

Explanation:

Start with x^2 - 8x - 10 = 18.

Simplify the constants by adding 10 to both sides: x^2 - 8x - 10 + 10 = 18 + 10.

Then x^2 - 8x = 28.

Now identify the coefficient of x. It is -8.

Take half of this, obtaining -4.

Square this result, obtaining 16.

Add 16, and then subtract 16, to x^2 - 8x:

x^2 - 8x + 16 - 16 = 28.

Add 16 to both sides:

x^2 - 8x + 16 = 28 + 16 = 44

Rewrite x^2 - 8x + 16 as (x - 4)², so that we have:

(x - 4)² = 44. This is in the form (x - p)² = 44, and matches Answer B.

Note: Please use " ^ " to indicate exponentiation: (x - 4)^2 = 44