Questions: 4x^2+24=0

Transcript text: 14. $4 x^{2}+24=0$

Solution

Solution Steps

Step 1: Set Up the Equation

We start with the equation given in the problem: \[ 4x^{2} + 24 = 0 \]

Step 2: Rearrange the Equation

To solve for $ x $, we first rearrange the equation by isolating the $ x^{2} $ term: \[ 4x^{2} = -24 \]

Step 3: Simplify the Equation

Next, we divide both sides of the equation by 4 to simplify: \[ x^{2} = -6 \]

Step 4: Solve for $ x $

To find $ x $, we take the square root of both sides. Since we have a negative number under the square root, we introduce the imaginary unit $ i $: \[ x = \pm \sqrt{-6} = \pm \sqrt{6}i \]

Step 5: Write the Final Solutions

Thus, the solutions to the equation are: \[ x = -\sqrt{6}i \quad \text{and} \quad x = \sqrt{6}i \]

Final Answer

$\boxed{x = \pm \sqrt{6}i}$

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Questions: 4x^2+24=0

Solution

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