Question

solve ((w - 2)^2 - 48 = 0), where (w) is a real number. simplify your answer as much as possible. if there is more than one solution, separate them with commas. if there is no solution, click
o solution.\ (w=square)

Explanation:

Step1: Isolate the squared term

Add 48 to both sides.
$$(w-2)^2 = 48$$

Step2: Take square roots of both sides

Use square root property for equations.
$$w-2 = \pm\sqrt{48}$$

Step3: Simplify the radical

Factor 48 into perfect square and remainder.
$$\sqrt{48} = \sqrt{16\times3} = 4\sqrt{3}$$

Step4: Solve for w

Add 2 to both sides.
$$w = 2 \pm 4\sqrt{3}$$

Answer:

$2 + 4\sqrt{3}, 2 - 4\sqrt{3}$