Question

question
solve the following quadratic equation for all values of $x$ in simplest form.
$3(x^2 - 6) - 2 = 1$
answer attempt 1 out of 2
additional solution $circ$ no solution
$x = $

Explanation:

Step1: Simplify the equation

$3(x^2 - 6) - 2 = 1$
$3(x^2 - 6) = 1 + 2$
$3(x^2 - 6) = 3$

Step2: Isolate the quadratic term

$x^2 - 6 = \frac{3}{3}$
$x^2 - 6 = 1$

Step3: Solve for $x^2$

$x^2 = 1 + 6$
$x^2 = 7$

Step4: Find square roots

$x = \pm\sqrt{7}$

Answer:

$x = \sqrt{7}$ and $x = -\sqrt{7}$