# Question Video: Solving Quadratic Equations with Complex Roots Mathematics

Find the solution set of π₯Β² + 8π₯ + 185 = 0 given π₯ β β.

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### Video Transcript

Find the solution set of π₯ squared plus eight π₯ plus 185 equals zero, given that π₯ is in the complex numbers.

We can use the quadratic formula to solve for the solution set. For an equation ππ₯ squared plus ππ₯ plus π equals zero, we can take negative π plus or minus the square root of π squared minus four ππ all divided by two π. So for our equation π₯ squared plus eight π₯ plus 185, π is one, π is eight, and π is 185. So we plug in one for π, eight for π, and 185 for π.

Now we have negative eight plus or minus the square root of 64 minus 740 divided by two. 64 minus 740 is negative 676. And since we have a negative underneath the square root, weβre gonna have an imaginary number. So weβre gonna have an π. So we have negative eight plus or minus 26π divided by two.

Since negative eight and 26 are both divisible by two, we get negative four plus or minus 13π. So our final answer is negative four plus 13π and negative four minus 13π.