Question

question
solve the following quadratic equation for all values of $x$ in simplest form.
$3(x - 7)^2 - 22 = 26$
answer attempt 1 out of 2
additional solution no solution
$x = $
$pm$ $sqrt{}$

Explanation:

Step1: Isolate the squared term

Add 22 to both sides:
$3(x-7)^2 = 26 + 22$
$3(x-7)^2 = 48$

Step2: Simplify the equation

Divide both sides by 3:
$(x-7)^2 = \frac{48}{3}$
$(x-7)^2 = 16$

Step3: Take square roots

Take square root of both sides:
$x-7 = \pm\sqrt{16}$
$x-7 = \pm4$

Step4: Solve for x

Solve for two cases:
Case 1: $x-7 = 4$ → $x = 4 + 7 = 11$
Case 2: $x-7 = -4$ → $x = -4 + 7 = 3$

Answer:

$x=11$ and $x=3$