Question

Solve quadratic equation $x^2-6x+9=12$using square root property

Short answer

The values of $x$are $3+2\sqrt{3}$and $3-2\sqrt{3}$.

Step-by-step solution

Step 1. Given information

The quadratic equation$x^2-6x+9=12$

Step 2. Factor the perfect square trinomial

$\Rightarrow {\left(x-3\right)}^2=12$

Step 3. Use square root property

$\Rightarrow x-3=\pm 2\sqrt{3}$

$\Rightarrow x=3\pm 2\sqrt{3}$

$\Rightarrow x=3+2\sqrt{3}$and$x=3-2\sqrt{3}$