Question

1. 18 - x² = 39

Explanation:

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

Subtract 18 from both sides of the equation \(18 - x^2 = 39\).
\(18 - x^2 - 18=39 - 18\)
Simplifying both sides, we get \(-x^2 = 21\).

Step2: Solve for \(x^2\)

Multiply both sides by - 1 to make the coefficient of \(x^2\) positive.
\((-1)\times(-x^2)=(-1)\times21\)
Which gives \(x^2=- 21\).

Step3: Analyze the solution in real numbers

For any real number \(x\), the square of \(x\) (i.e., \(x^2\)) is always non - negative (i.e., \(x^2\geq0\)). But here we have \(x^2=-21\), and \(-21<0\). So, there is no real solution for \(x\) in the set of real numbers. If we consider complex numbers, we can write \(x=\pm\sqrt{- 21}=\pm i\sqrt{21}\), where \(i\) is the imaginary unit with \(i^2=-1\).

Answer:

There is no real solution. In the complex number system, \(x = \pm i\sqrt{21}\)