Easy Algebra Step-by-Step

Solving Quadratic Equations 165

When the coeffi cient b of a quadratic equation is not 0, the quick solution

method does not work. Instead, you have three common methods for solving

the equation: (1) by factoring, (2) by completing the square, and (3) by using

the quadratic formula.

Solving Quadratic Equations by Factoring

When you solve quadratic equations by factoring, you use the following

property of 0.

Zero Factor Property

If the product of two numbers is 0, then at least one of the numbers is 0.

Problem Solve by factoring.

a. xx^2 + 202 xx

b. xx^2 +=x 6

c. xx^244 xx

Solution

a. xx^2 + 202 xx

Step 1. Put the equation in standard form.

xx^2 + 202 xx is in standard form because only a zero term is on the

right side.

Step 2. Use the distributive property to factor the left side of the equation.

x()x ))= 0

Step 3. Use the zero factor property to separate the factors.

Thus, x= 0 or x+ 20 =.

Step 4. Solve the resulting linear equations.

The solution is x=^0 or x=−^2.

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