How to Find All Real Solutions of an Equation

Learn how to solve linear equations by practicing the various approaches.
••• Comstock/Comstock/Getty Images

Frequently, in Algebra class, you will be called to find all "real solutions" of an equation. Such questions essentially are asking you to find all solutions of an equation, and should any imaginary solutions (containing the imaginary number 'i') come up, to discard these solutions. Therefore, most of the time, you will approach both equations with only real solutions and equations with both real and imaginary solutions the same way: find the solutions, and discard the ones that are not real numbers.

    Simplify the equation as much as possible. For instance, if given the equation x4 + x2 - 6 = 0, you can use a u-substitution to simplify and then factor. If x2=u, then the equation becomes u2+u-6=0.

    Factor the simplified equation. You can rewrite the equation in Step 1 as u2+3u-2u-6=0, then rewrite as u(u+3)-2(u+3)=0, which becomes (u-2)(u+3)=0.

    Find the roots of the factored equation. Here, they are u=2 and u=3. Since x2=u, x must equal +/- sqrt(2), and +/- sqrt(3).

    Discard any imaginary solutions, such as the square root of a negative number. Here, there are no imaginary solutions.

Related Articles

How to Know when an Equation has NO Solution, or Infinitely...
How to Solve Equations in the Real Number System
How to Find X-Intercept & Y-Intercept
How to Find The Square Root of a Number
How to Solve a Parabola
How to Know when an Equation has NO Solution, or Infinitely...
Algebra 1 Substitution Method
How to Write an Absolute-Value Equation That Has Given...
What Is the Difference Between a Quadratic and a Linear...
How to Factorise in Math
How to Solve Binomial Equations by Factoring
How to Convert Slope Intercept Form to Standard Form
How to Find the Domain of a Square Root Function
What Are the X-Intercept & Y-Intercept of a Linear...
How to Identify a Numerical Coefficient of a Term
How to Find a Fraction of a Number
Differences Between Absolute Value & Linear Equations
How to Find B in Y=Mx + B
How to Multiply Fractions With Mixed Numbers
How to Find the Domain of a Fraction

Dont Go!

We Have More Great Sciencing Articles!