Questions: Solve the equation. Simplify solutions and list from least to greatest, separated by a comma. 3 x^2+48=0

Solution Steps

To solve the quadratic equation \(3x^2 + 48 = 0\), we first isolate the \(x^2\) term by subtracting 48 from both sides and then dividing by 3. Next, we take the square root of both sides to solve for \(x\). Since the equation involves a negative number under the square root, the solutions will be complex numbers. Finally, we simplify the solutions and list them from least to greatest.

Starting with the equation \(3x^2 + 48 = 0\), we isolate the \(x^2\) term by subtracting 48 from both sides: \[ 3x^2 = -48 \]

Next, we divide both sides by 3 to simplify: \[ x^2 = -16 \]

Taking the square root of both sides, we find: \[ x = \pm \sqrt{-16} = \pm 4i \] This gives us the two complex solutions: \(x_1 = 4i\) and \(x_2 = -4i\).

We list the solutions from least to greatest: \[ x_2 = -4i, \quad x_1 = 4i \]

Final Answer