Question

question
solve the following quadratic equation for all values of $x$ in simplest form.
$3(x - 9)^2 = 27$
answer attempt 1 out of 2
additional solution no solution
$x = $
submit answer

Explanation:

Step1: Divide both sides by 3

$\frac{3(x-9)^2}{3}=\frac{27}{3}$
Simplifies to: $(x-9)^2=9$

Step2: Take square root of both sides

$\sqrt{(x-9)^2}=\pm\sqrt{9}$
Simplifies to: $x-9=\pm3$

Step3: Solve for x (positive case)

$x-9=3$
$x=3+9$
Simplifies to: $x=12$

Step4: Solve for x (negative case)

$x-9=-3$
$x=-3+9$
Simplifies to: $x=6$

Answer:

$x=12$ and $x=6$