Questions: Solve. 4 x^2 - 28 = 0

Transcript text: Solve. \[ 4 x^{2}-28=0 \]

Solution

Solution Steps

To solve the quadratic equation \(4x^2 - 28 = 0\), we can first isolate the \(x^2\) term by adding 28 to both sides and then dividing by 4. After that, we take the square root of both sides to solve for \(x\).

Step 1: Set Up the Equation

We start with the quadratic equation: \[ 4x^2 - 28 = 0 \]

Step 2: Isolate \(x^2\)

To isolate \(x^2\), we add 28 to both sides: \[ 4x^2 = 28 \]

Step 3: Divide by 4

Next, we divide both sides by 4: \[ x^2 = 7 \]

Step 4: Take the Square Root

Taking the square root of both sides gives us: \[ x = \pm \sqrt{7} \]

Final Answer

The solutions to the equation are: \[ \boxed{x = 2.6458} \quad \text{and} \quad \boxed{x = -2.6458} \]

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