Question

Solve the following equation by completing the square. 4 ⁢ x 2 − 16 ⁢ x + 8 = 0

Answer 1

Answer: x= 2 -√2 and x = 2 ± √2

Explanation:

Divide both sides of the equation by 4 to get x^2 - 4x + 2 = 0.

Move the constant term to the right side of the equation to get x^2 - 4x = -2.

Add the square of half of the coefficient of x to both sides of the equation to get x^2 - 4x + 4 = -2 + 4. This makes the left side a perfect square trinomial.

Factor the left side of the equation and simplify the right side to get (x - 2)^2 = 2.

Take the square root of both sides of the equation to get x - 2 = ±√2.

Add 2 to both sides of the equation to get x = 2 ±√2.

Therefore, the solutions are x = 2 +√2 and x = 2 -√2.

Answer 2

Explanation:

To solve the equation 4 ⁢ x 2 − 16 ⁢ x + 8 = 0 by completing the square, we first divide both sides by 4 to get x^2 - 4x + 2 = 0.

Then we add (b/2)^2 to both sides of the equation where b is the coefficient of x. In this case, b = -4.

So we add (-4/2)^2 = 4 to both sides of the equation.

This gives us

x^2 - 4x + 6 = 4.

We can then write this as

(x - 2)^2 = 2.

Taking the square root of both sides gives us

x - 2 = ±√2.

Solving for x gives us

x = 2 ± √2.