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Intermediate Algebra – Student Workbook – Second Edition 2013

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Lesson 5b - Solving Quadratic Equations<br />

Mini-Lesson<br />

Problem 7 WORKED EXAMPLE<strong>–</strong>SOLVE QUADRATIC EQUNS USING<br />

QUADRATIC FORMULA<br />

Solve the quadratic equation by using the Quadratic Formula. Verify your result by graphing and<br />

using the Intersection method.<br />

Solve 3x 2 <strong>–</strong> 2 = -x using the quadratic formula.<br />

1. Set to zero and write in standard form 3x 2 + x - 2 = 0<br />

2. Identify a = 3, b = 1, and c = -2<br />

3.<br />

(1) <br />

x <br />

(1)<br />

2<br />

2(3)<br />

4(3)( 2)<br />

1<br />

1<br />

( 24)<br />

<br />

6<br />

1<br />

1<br />

24<br />

<br />

6<br />

1<br />

<br />

6<br />

25<br />

4. Make computations for x 1 and x 2 as below and note the complete simplification process:<br />

1<br />

25 1<br />

5 4<br />

So, x <br />

6 6 6<br />

1<br />

25 1<br />

5 6<br />

x <br />

6 6 6<br />

1<br />

<br />

2<br />

<br />

2<br />

3<br />

1<br />

Final solution x = 2 , x = -1 (be sure to verify graphically…you may also need to obtain a<br />

3<br />

decimal approximation for a given value depending on how you are asked to leave your final<br />

answer)<br />

Graphical verification of Solution x = 2 3 Graphical verification of Solution x = -1<br />

[Note that 2 . 6666667 ] 3<br />

You can see by the graphs above that this equation is an example of the “Case 2” possibility of<br />

two, unique real number solutions for a given quadratic equation.<br />

Scottsdale Community College Page 220 <strong>Intermediate</strong> <strong>Algebra</strong>

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