Question

question
solve the following quadratic equation for all values of $x$ in simplest form.
$3(x - 8)^2 - 11 = 40$
answer attempt 1 out of 2
additional solution $\bigcirc$ no solution
$x = $
$pm$ $sqrt{}$

Explanation:

Step1: Isolate the squared term

Add 11 to both sides:
$3(x-8)^2 = 40 + 11$
$3(x-8)^2 = 51$

Step2: Simplify the equation

Divide both sides by 3:
$(x-8)^2 = \frac{51}{3}$
$(x-8)^2 = 17$

Step3: Take square roots

Take square root of both sides:
$x-8 = \pm\sqrt{17}$

Step4: Solve for x

Add 8 to both sides:
$x = 8 \pm\sqrt{17}$

Answer:

$x = 8 + \sqrt{17}$ and $x = 8 - \sqrt{17}$