Answer:
C. x = 8 only
Explanation:
Given the quadratic equation:
[tex]x^2-16x+64=0[/tex]
To solve for , we facotorize.
Step 1: Multiply the coefficient of x² and the constant.
[tex]64\times1=64[/tex]
Step 2: Find two numbers that multiply to give 64, and add to give the coefficient of x, -16.
[tex]\begin{gathered} -8-8=-16 \\ (-8)(-8)=64 \end{gathered}[/tex]
Step 3: Rewrite the middle with those numbers.
[tex]x^2-8x-8x+64=0[/tex]
Step 4: Factor the first two and last two terms separately.
Ensure that the expression in the brackets is the same.
[tex]\begin{gathered} x(x-8)-8(x-8)=0 \\ (x-8)(x-8)=0 \end{gathered}[/tex]
Step 5: Solve for x
[tex]\begin{gathered} x-8=0\;or\;x-8=0 \\ x=8\text{ \lparen twice\rparen} \end{gathered}[/tex]
The solution(s) to x² – 16x+64 = 0 is x = 8 only.
Option C is correct.
