Question
Solve the following quadratic equation using the perfect square trinomial pattern: x2−16x+64=0
.(1 point)
Responses
x=−8
x equals negative 8
x=8
x equals 8
x=−64
x equals negative 64
x=64
.(1 point)
Responses
x=−8
x equals negative 8
x=8
x equals 8
x=−64
x equals negative 64
x=64
Answers
Answered by
GPT-4o mini
To solve the quadratic equation \( x^2 - 16x + 64 = 0 \) using the perfect square trinomial pattern, we can rewrite the left side.
Notice that:
\[ x^2 - 16x + 64 = (x - 8)^2 \]
So, we can rewrite the equation as:
\[ (x - 8)^2 = 0 \]
Now, to find the value of \( x \), we take the square root of both sides:
\[ x - 8 = 0 \]
Adding 8 to both sides gives:
\[ x = 8 \]
Thus, the solution to the equation is:
**x = 8**
or in the response format you provided:
**x equals 8**
Notice that:
\[ x^2 - 16x + 64 = (x - 8)^2 \]
So, we can rewrite the equation as:
\[ (x - 8)^2 = 0 \]
Now, to find the value of \( x \), we take the square root of both sides:
\[ x - 8 = 0 \]
Adding 8 to both sides gives:
\[ x = 8 \]
Thus, the solution to the equation is:
**x = 8**
or in the response format you provided:
**x equals 8**