Question

x² - 2x + 5 = 0

Explanation:

Step1: Identify the quadratic equation form

The equation is \(x^2 - 2x + 5 = 0\), which is in the form \(ax^2 + bx + c = 0\) where \(a = 1\), \(b=-2\), \(c = 5\).

Step2: Use the quadratic formula

The quadratic formula is \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). First, calculate the discriminant \(\Delta=b^2-4ac\).

Substitute \(a = 1\), \(b=-2\), \(c = 5\) into the discriminant formula:
\(\Delta=(-2)^2-4\times1\times5=4 - 20=-16\)

Step3: Solve for \(x\)

Since \(\Delta=-16\), we have \(x=\frac{-(-2)\pm\sqrt{-16}}{2\times1}=\frac{2\pm4i}{2}=1\pm2i\)

Answer:

The solutions are \(x = 1 + 2i\) and \(x = 1 - 2i\)