Question

17.) -3(x + 1)² = 240

Explanation:

Step1: Divide both sides by -8

To isolate the squared term, we divide each side of the equation \(-8(x + 1)^2 = 240\) by \(-8\). This gives us \((x + 1)^2=\frac{240}{-8}=-30\).

Step2: Analyze the result

The square of a real number \((x + 1)^2\) must be non - negative (since for any real number \(a\), \(a^2\geq0\)). But we have \((x + 1)^2=-30\), and \(-30\) is negative. In the set of real numbers, there is no real number \(x\) such that when we square \(x + 1\) we get a negative number.

Answer:

There is no real solution for \(x\) in the equation \(-8(x + 1)^2 = 240\). If we consider complex numbers, we can solve it as follows:
From \((x + 1)^2=-30\), we take the square root of both sides. \(x + 1=\pm\sqrt{-30}=\pm i\sqrt{30}\) (where \(i=\sqrt{-1}\) is the imaginary unit). Then \(x=-1\pm i\sqrt{30}\).