Question

Use a calculator to solve the equation or write no solution. Round the results to the nearest hundredth. $$3 x^{2}+7=31$$

Short answer

The solution to the equation is \(x = 2.83\) and \(x = -2.83\).

Step-by-step solution

Isolate \(x^2\)

First, subtract 7 from both sides of the equation: \(3x^2 + 7 - 7 = 31 - 7\). This leaves you with \(3x^2 = 24\).

Solve for \(x^2\)

Divide both sides of the equation by 3: \(\frac{3x^2}{3} = \frac{24}{3}\). Now we are left with \(x^2 = 8\).

Find \(x\)

Next, we need to find the square roots of 8 since \(x^2 = 8\). Remember that a square root has both a positive and a negative value. Therefore, \(x = \pm \sqrt{8}\). We then use a calculator to find the numerical values for \(\sqrt{8}\). This will give \(\pm 2.83\) (rounded to the nearest hundredth).