Questions: What are the solutions to 2x^2-8=0 when solved by taking the square roots?

Transcript text: What are the solutions to $2 x^{2}-8=0$ when solved by taking the square roots?

Solution

Step 1: Set the equation to zero

We start with the given equation: \[ 2x^2 - 8 = 0 \]

Step 2: Isolate the quadratic term

Add 8 to both sides of the equation to isolate the quadratic term: \[ 2x^2 = 8 \]

Step 3: Divide by the coefficient of $x^2$

Divide both sides by 2 to solve for $x^2$: \[ x^2 = 4 \]

Step 4: Take the square root of both sides

Take the square root of both sides to solve for $x$: \[ x = \pm \sqrt{4} \] \[ x = \pm 2 \]

The solutions to the equation $2x^2 - 8 = 0$ are: \[ \boxed{x = 2 \text{ and } x = -2} \]

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