Solve the following quadratic equation using the perfect square trinomial pattern: x2−12x+36 (1 point) Responses x=−6 x is equal to negative 6 x=6 x is equal to 6 x=−12 x is equal to negative 12 x=12

Answer 1

To solve the quadratic equation \(x^2 - 12x + 36\) using the perfect square trinomial pattern, we can rewrite the equation in the form \((x - a)^2 = 0\):

1. Identify the perfect square trinomial: \(x^2 - 12x + 36\) can be factored as: \[ (x - 6)^2 \]

2. Set the equation equal to zero: \[ (x - 6)^2 = 0 \]

3. Solve for \(x\) by taking the square root of both sides: \[ x - 6 = 0 \]

4. Therefore: \[ x = 6 \]

So the solution to the quadratic equation \(x^2 - 12x + 36 = 0\) is: \[ x = 6 \]

The appropriate response is: x = 6.