Question

what method would you choose to solve the equation $2x^2 - 7 = 9$? explain why you chose this method.

Explanation:

Step1: Isolate the quadratic term

First, we want to get the \(x^2\) term by itself. So we add 7 to both sides of the equation \(2x^2 - 7 = 9\).
\[2x^2 - 7 + 7 = 9 + 7\]
Simplifying both sides, we get:
\[2x^2 = 16\]

Step2: Solve for \(x^2\)

Next, we divide both sides by 2 to solve for \(x^2\).
\[\frac{2x^2}{2} = \frac{16}{2}\]
Simplifying, we have:
\[x^2 = 8\]

Step3: Solve for \(x\)

Now, to find \(x\), we take the square root of both sides. Remember that when we take the square root of a number, we get both a positive and a negative solution.
\[x = \pm\sqrt{8}\]
We can simplify \(\sqrt{8}\) as \(2\sqrt{2}\), so:
\[x = \pm 2\sqrt{2}\]

I chose this method (isolation of the quadratic term followed by square root) because the equation is a simple quadratic equation with no linear term (the term with \(x\) to the first power). This method is straightforward for such equations where we can easily isolate \(x^2\) and then take the square root to find the solutions.

Answer:

The method used is isolating the quadratic term and then taking the square root. The solutions are \(x = 2\sqrt{2}\) and \(x = -2\sqrt{2}\) (or \(x \approx \pm 2.828\) if decimal approximations are preferred).