Question

Use a calculator to solve the equation or write no solution. Round the results to the nearest hundredth. $$2 x^{2}-4=10$$

Short answer

The solutions to the equation \(2x^{2} - 4 = 10\) are \(x = 2.65\) and \(x = -2.65\), when rounded to the nearest hundredth.

Step-by-step solution

Rearrange the equation to solve for 'x'

To start off, the first step is to isolate \(x^{2}\). This is done by adding '4' to both sides of the equation so that it looks like this: \(2x^{2} = 14\).

Divide both sides of the equation by 2

Next, both sides of the equation are divided by 2, to isolate the \(x^{2}\) further, thus getting: \(x^{2} = 7\).

Take the square root of both sides

In order to solve for x, we need to take square roots of both sides of the equation. However, understanding that \(x^{2}\) would result in a positive or a negative value results in the equation being expressed as, \(x=\sqrt{7}\) or \(x=-\sqrt{7}\).

Use a calculator to find the square root of 7 to two decimal places

By inputting \(\sqrt{7}\) in a calculator, we get approximately 2.65. Similarly, when we input \(-\sqrt{7}\), we get -2.65. The final result is hence, \(x = 2.65\) or \(x = -2.65\) when rounded to the nearest hundredth.