Question

Write x^2-2x-6 in the form (x+c)^2+d

A) What are the values of C and D?

B) Using your answer to part a), solve x^2-2x-6=0, giving your answers in the form x=f+-sqrt{g} where f and g are integers.

Answer 1

A) To write the expression x^2 - 2x - 6 in the form (x + c)^2 + d, we need to complete the square.

First, let's rewrite the expression:

x^2 - 2x - 6 = (x^2 - 2x + 1) - 1 - 6 = (x - 1)^2 - 7

From the above expression, we can see that the values of C and D are:

C = 1

D = -7

B) Now that we have the expression x^2 - 2x - 6 in the form (x + C)^2 + D, we can solve the equation x^2 - 2x - 6 = 0.

(x - 1)^2 - 7 = 0

(x - 1)^2 = 7

Taking the square root of both sides:

x - 1 = ±√7

Solving for x:

x = 1 ± √7

Therefore, the solutions to the equation x^2 - 2x - 6 = 0 are:

x = 1 + √7 and x = 1 - √7