Solving Quadratic Equations Using Patterns Quick Check

Question

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Question
Solve the following quadratic equation using the perfect square trinomial pattern: x2−16x+64=0.(1 point)
Responses

x=−64
x equals negative 64

x=64
x equals 64

x=8
x equals 8

x=−8
x equals negative 8
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Answer 1

To solve the quadratic equation \(x^2 - 16x + 64 = 0\) using the perfect square trinomial pattern, we recognize that the equation can be factored as:

\[ (x - 8)^2 = 0 \]

Next, we take the square root of both sides:

\[ x - 8 = 0 \]

Now, we solve for \(x\):

\[ x = 8 \]

So, the solution to the equation is:

x = 8 (Option: x equals 8)