Question

question
solve the following quadratic equation for all values of $x$ in simplest form.
$3(x - 7)^2 + 16 = 46$
answer attempt 1 out of 2
○ additional solution ○ no solution
$x = $
$pm$ $sqrt{ }$

Explanation:

Step1: Isolate the squared term

Subtract 16 from both sides:
$3(x-7)^2 = 46 - 16$
$3(x-7)^2 = 30$

Step2: Simplify the equation

Divide both sides by 3:
$(x-7)^2 = \frac{30}{3}$
$(x-7)^2 = 10$

Step3: Take square roots of both sides

Apply square root property:
$x-7 = \pm\sqrt{10}$

Step4: Solve for x

Add 7 to both sides:
$x = 7\pm\sqrt{10}$

Answer:

$x = 7+\sqrt{10}$ and $x = 7-\sqrt{10}$