Question

solve the following equation using the square root property. 3x² - 3 = -30

Explanation:

Step1: Isolate the \(x^2\) term

First, we add 3 to both sides of the equation \(3x^2 - 3=-30\) to get:
\(3x^2=-30 + 3\)
\(3x^2=-27\)
Then, divide both sides by 3:
\(x^2=\frac{-27}{3}\)
\(x^2=- 9\)

Step2: Apply the square root property

The square root property states that if \(x^2 = a\), then \(x=\pm\sqrt{a}\). But here \(a=-9\). In the set of real numbers, the square root of a negative number is not defined. However, if we consider complex numbers, we know that \(\sqrt{-1}=i\), so:
\(x=\pm\sqrt{-9}=\pm\sqrt{9\times(- 1)}=\pm(3i)\)

Answer:

The solutions are \(x = 3i\) and \(x=-3i\) (in the complex number system). If we are restricted to real numbers, there is no real solution.