Question

Consider the equation: 24=x^2-4x-3. 1) Rewrite the equation by completing the square. Your equation should look like (x-c)^2=d or (x-c)^2=d. 2) What are the solutions to the equation? Choose 1 answer: (Choice a) x=2±5, (Choice b) x=-2±5, (Choice c) x=2±√5, (Choice d) x=-2±√5.

Answer 1

By completing the square, the given equation is rewritten as (x - 2)^2 = 31, leading to the solutions x = 2 ± √31, which do not match any of the choices offered.

Step-by-step explanation:

To rewrite the equation 24 = x^2 - 4x - 3 by completing the square, we first need to get the equation in the form x^2 - 4x = d. Move the constant term to the other side by adding 3 to both sides:

x^2 - 4x = 27

Now, to complete the square, we take half of the coefficient of x, which is -2 (-4/2 = -2), square it, and add it to both sides of the equation:

x^2 - 4x + 4 = 27 + 4

x^2 - 4x + 4 = 31

Now we can write the left side of the equation as a square:

(x - 2)^2 = 31

To find the solutions to the equation (x-2)^2 = 31, we take the square root of both sides:

x - 2 = ±5√31

Add 2 to both sides:

x = 2 ± √31

Therefore, the solutions to the equation are x = 2 ± √31, which corresponds to none of the choices given, indicating a potential typo in the options provided or in the equation itself.