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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

Find The Solutions To X2 16x64 0O A X2 And X 32O B X 8 And X 8O C X 8 OnlyO D X 4 And X 16 class=

Sagot :

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.

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