Question

solve the equation using the method of your choice
y² - 10y + 50 = 0

Explanation:

Step1: Identify coefficients for quadratic formula

For quadratic equation \(ay^2 + by + c = 0\), here \(a = 1\), \(b=-10\), \(c = 50\).

Step2: Apply quadratic formula \(y=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)

First, calculate discriminant \(D=b^2 - 4ac=(-10)^2-4\times1\times50 = 100 - 200=-100\).
Then, \(y=\frac{-(-10)\pm\sqrt{-100}}{2\times1}=\frac{10\pm10i}{2}\).

Step3: Simplify the expression

Divide numerator terms by 2: \(y = 5\pm5i\).

Answer:

\(y = 5 + 5i\) or \(y = 5 - 5i\)