Solving Equations In Quadratic Form - PowerPoint PPT Presentation

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Solving Equations In Quadratic Form

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  1. Solving Equations In Quadratic Form • There are several methods one can use to solve a quadratic equation. Sometimes we are called upon to solve an equation that is in Quadratic Form. • A quadratic equation is an equation that can be simplified into the form … • An equation in quadratic form can be simplified into the form …

  2. Example 1: Solve the equation Move all terms to the left side. This equation is now in quadratic form.

  3. We will solve the equation with what is called a u-substitution. Let u = expression. The equation now takes the form of a quadratic equation by substituting u for the expression.

  4. Solve the quadratic equation.

  5. Since the original equation was in variable x, our solutions need to be in variable x. Taking the solutions of u and combining them with the original u-substitution equation we get …

  6. Solving these two quadratic equations … … we now have the solution to the original equation.

  7. Example 2: Solve the equation Note that this equation is in quadratic form.

  8. Use a u-substitution. Let u = expression. The equation now takes the form of a quadratic equation by substituting u for the expression.

  9. Solve the quadratic equation.

  10. Since the original equation was in variable x, our solutions need to be in variable x. Taking the solutions of u and combining them with the original u-substitution equation we get …

  11. Solving the first equation …

  12. Solving the second equation …

  13. The solutions to the original equation are …

  14. END OF PRESENTATION