Question

Solve the equation algebraically. Check the solutions graphically. $$ 2 x^{2}=32 $$

Short answer

The algebraic solutions for the equation are \(x=4\) and \(x=-4\).

Step-by-step solution

Simplify the equation

The given equation is \(2 x^{2}=32\). To isolate \(x^{2}\), divide both sides of the equation by 2. The simplified equation is \(x^{2}=16\).

Solve for x

To solve for 'x', take the square root of both sides. Remember that when you take the square root of a value, there is a positive and a negative solution. After taking the square root, you get \(x=4\) and \(x=-4\).

Check solutions graphically

On plotting the equation \(y=2x^{2}\), it can be noticed that the parabola intersects the x-axis at the points \(x=4\) and \(x=-4\). This graphically verifies the solution obtained algebraically.