How to Solve Equations in the Real Number System

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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.

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