Easy Algebra Step-by-Step

Solving Quadratic Equations 167

Solution

Step 1. Complete the square on the left side by adding the square of

1

2

the

coeffi cient of x, being sure to maintain the balance of the equation

by adding the same quantity to the right side.

xx^226 xx +

xx^226 xx + 1

Step 2. Factor the left side.

())))))(()(((( = 7

()))^2 = 7

Step 3. Solve using the quick solution method.

x+ 17 =±

x=− 17 ±

Thus, x=− 17 + or x=− 17 −.

Solving Quadratic Equations by Using the Quadratic Formula

Having illustrated several useful approaches, it turns out there is one tech-

nique that will always solve any quadratic equation that is in standard form.

This method is solving by using the quadratic formula.

Quadratic Formula

The solution of the quadratic equation ax^2 ++bxbx c= 0 is given by the

formula x bbac

a

=−b −

(^24)
2

. The term under the radical, ba^2 c, is called

the discriminant of the quadratic equation.

If ba^2 aaccc 0 , there is only one root for the equation. If ba^2 aaccc 0 ,

there are two real number roots. And if ba^2 aaccc 0 , there is no real number

solution. In the latter case, both roots are complex numbers because this

solution involves the square root of a negative number.

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