Question

Find the solution(s) to x^2 – 16x+64 = 0.-O A. x=-2 and x = 32O B. x = 8 and x = -8O C. x = 8 onlyO D. x = 4 and x = 16

Answer 1

C. x = 8 only

Explanation:

Given the quadratic equation:

`x^2-16x+64=0`

To solve for , we facotorize.

Step 1: Multiply the coefficient of x² and the constant.

`64*1=64`

Step 2: Find two numbers that multiply to give 64, and add to give the coefficient of x, -16.

`\begin{gathered} -8-8=-16 \\ (-8)(-8)=64 \end{gathered}`

Step 3: Rewrite the middle with those numbers.

`x^2-8x-8x+64=0`

Step 4: Factor the first two and last two terms separately.

Ensure that the expression in the brackets is the same.

`\begin{gathered} x(x-8)-8(x-8)=0 \\ (x-8)(x-8)=0 \end{gathered}`

Step 5: Solve for x

`\begin{gathered} x-8=0\;or\;x-8=0 \\ x=8\text{ \lparen twice\rparen} \end{gathered}`

The solution(s) to x² – 16x+64 = 0 is x = 8 only.

Option C is correct.