Question

Use completing the square to solve for x:x²-16x-8=0.

a) x=8
b) x=-8
c) x=4
d) x=-4

Answer 1

The correct answer is none of the above. To solve the quadratic equation x² - 16x - 8 = 0 using completing the square, follow the steps: move the constant term, square the coefficient, add the squared value, factor the perfect square trinomial, take the square root, simplify, and solve for x.

Step-by-step explanation:

To solve the quadratic equation x² - 16x - 8 = 0 using completing the square:

1. Move the constant term to the right side of the equation: x² - 16x = 8.
2. Take half of the coefficient of x and square it: (16/2)² = 64.
3. Add the squared value to both sides of the equation: x² - 16x + 64 = 8 + 64.
4. Factor the left side of the equation which is now a perfect square trinomial: (x - 8)² = 72.
5. Take the square root of both sides of the equation: x - 8 = ±√72.
6. Simplify the square roots: x - 8 = ±6√2.
7. Add 8 to both sides of the equation: x = 8 ± 6√2.

So the correct option is: x = 8 ± 6√2.