Question

7x² - 2 = -65

Explanation:

Step1: Add 2 to both sides

To isolate the term with \(x^2\), we add 2 to both sides of the equation \(7x^2 - 2 = -65\). This gives us \(7x^2 - 2 + 2 = -65 + 2\), which simplifies to \(7x^2 = -63\).

Step2: Divide both sides by 7

Next, we divide both sides of the equation \(7x^2 = -63\) by 7. So, \(\frac{7x^2}{7}=\frac{-63}{7}\), which simplifies to \(x^2 = -9\).

Step3: Analyze the solution for real numbers

For real numbers, the square of any real number \(x\) (i.e., \(x^2\)) is always non - negative (greater than or equal to 0). But here we have \(x^2=-9\), and - 9 is negative. So, there is no real solution for this equation. If we consider complex numbers, we can write \(x = \pm\sqrt{-9}=\pm3i\), where \(i\) is the imaginary unit with \(i^2=-1\).

Answer:

If we are looking for real solutions, there is no solution. If we consider complex solutions, \(x = 3i\) or \(x=-3i\) (where \(i=\sqrt{-1}\))