Question

Which statements are true when solving x^2 - 8x + 16 = 0?

A) x + 4 = 0
B) Factor to solve.
C) x = 4 is a double root.
D) Complete the square to solve.
E) The equation is a perfect square trinomial.

Answer 1

The correct answer is D) Complete the square to solve.

Step-by-step explanation:

The quadratic formula can be used to solve the equation x^2 - 8x + 16 = 0. However, completing the square is a more efficient method for this particular equation.

Steps to solve:

1. Move the constant term to the right side of the equation:

x^2 - 8x = -16

2. Divide both sides by the coefficient of the x^2 term:

x^2 - 8x = -16

3. Complete the square:

(x^2 - 8x) + 16 = -16 + 16

4. Factor the left side of the equation:

(x - 4)^2 = 0

5. Take the square root of both sides:

x - 4 = 0

6. Solve for x:

x = 4

Therefore, x = 4 is the solution to the equation x^2 - 8x + 16 = 0. Completing the square was an efficient method for solving this equation.