How to Solve Equations in the Real Number System

By Tricia Lobo; Updated April 24, 2017
Equations with exponents can be difficult to solve.

Occasionally, in your study of algebra and higher-level math, you will come across equations with unreal solutions — for instance, solutions containing the number i, which is equal to sqrt(-1). In these instances, when you are asked to solve equations in the real number system, you will need to discard the unreal solutions and provide only the real number solutions. Once you understand the basic approach, these problems are relatively simple.

Factor the equation. For instance, you can rewrite the equation 2x^3+3x^2+2x+3=0 as x^2*(2x+3) + 1(2x+3)=0, then as (x^2+1)(2x+3)=0.

Obtain the roots of the equation. When you set the first factor, x^2+1 equal to 0, you will find x=+/- sqrt(-1), or +/-i. When you set the other factor, 2x+3 equal to 0, you will discover that x=-3/2.

Discard the unreal solutions. Here, you are left with only one solution: x=-3/2.

About the Author

Tricia Lobo has been writing since 2006. Her biomedical engineering research, "Biocompatible and pH sensitive PLGA encapsulated MnO nanocrystals for molecular and cellular MRI," was accepted in 2010 for publication in the journal "Nanoletters." Lobo earned her Bachelor of Science in biomedical engineering, with distinction, from Yale in 2010.