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       35–44 Simplify the radical expressions.

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       45–50 Simplify the complex numbers.

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      Solving Quadratic Equations and Nonlinear Inequalities

      A quadratic expression is one containing a term raised to the second power. When a quadratic expression is set equal to 0, you have an equation that has the possibility of two real solutions; for example, you may have an equation for which the answers are

. Nonlinear inequalities can have an infinite number of solutions, so those answers are written with expressions such as x > 8 or x > –2; these solutions can also be written using interval notation.

      In this chapter, you’ll work with quadratic equations and inequalities in the following ways:

       Solving simple equations using the square root rule

       Rewriting quadratics as the product of two binomials in order to solve them

       Applying the quadratic formula

       Completing the square

       Solving quadratic-like equations

       Finding the solutions of quadratic and other nonlinear inequalities

      Don’t let common mistakes like the following ones trip you up when working with quadratic equations and inequalities:

       Forgetting to consider ±x when using the square root rule

       Reducing the fraction incorrectly when applying the quadratic formula

       Stopping too soon when solving quadratic-like equations

       Eliminating values as solutions when they create a 0 in the denominator of a fraction

       51–60 Solve the equations using the square root rule.

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       61–76 Solve the quadratic equations by factoring and applying the Multiplication Property of Zero.

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