Other Types of Equations 

-- Part 1.5 --
  Solve for x:  20x3 – 125x = 0

Solve

Step

Check 

20x3 – 125x = 0

5x(4x2 – 25) = 0

5x(2x – 5)(2x + 5) = 0

5x = 0 or 2x – 5 = 0 or 
2x + 5 = 0

x = 0 , x = 5/2 or x = -5/2

Try factoring.  It usually is the easiest method.

LCM = 5x

Keeping factoring.  Perfect Square Trinomial

Set each factor to zero

Click Solving Linear Equations for help

If x  = 0, then
20(0)3 – 125(0) = 0
    0  – 0 = 0

If x  = 5/2, then
20(5/2)3 – 125(5/2) = 0
    20(125/8)  – 125(5/2) = 0
625/2  – 625/2 = 0
   0 = 0

If x  = -5/2, then
20(-5/2)3 – 125(-5/2) = 0
    20(-125/8)  – 125(-5/2) = 0
-625/2  + 625/2 = 0
     0 = 0

     Solve for x:     36x3 – 64x = 0             [Solution]

 

 Solve for x:  2x3 + x2  – 2x – 1 = 0

Solve

Step

Check 

2x3 + x2  – 2x – 1 = 0

Use the grouping method
 

If x  = -½, then
2(-½)3+(-½)2–2(-½)–1=0
    2(-1/8)+¼+1–1 = 0
-¼ + ¼ = 0
0 = 0

If x  = 1, then
2(1)3+(1)2–2(1)–1 = 0
    2 + 1 – 2 –1 = 0
0 = 0

If x  = -1, then
2(-1)3+(-1)2–2(-1)–1 = 0
    -2 + 1 + 2 –1 = 0
0 = 0

x2 (2x + 1)  – 2x – 1 = 0

 Look for a pattern.  Factor a x2 form the first 2 terms.
 

x2 (2x + 1)  – 1(2x + 1) = 0

 I see a 2x + 1 pattern.  Factor out a -1 from the last 2 terms.
 
(2x + 1)(x2  – 1) = 0 Now factor out a (2x + 1) from each part.
 

(2x + 1)(x – 1)(x + 1) = 0

 Finish factoring!  Difference of two squares.
 

2x + 1 = 0 or x – 1 or 
x + 1 = 0 

 Set each factor to zero
 

x = -1/2 , x = 1 or x = -1

 Click Solving Linear Equations for help.
Use grouping to solve a cubic equation with 4 terms.  If this doesn't work then we are stuck for now.  Try it with 4th degree equations too.

      Solve for x:  x3 + 3x2  – 4x – 12 = 0 [Solution]

 

   Solve for x: 

Solve

Step

Check 

Add 3 to both sides.

If x  = -4, then

Square both sides to undo the square root.
1 – 2x = 9 Solve for x.
-2x = 8 Click Solving Linear Equations for help.
x = -4 Done!!
                            Note:  

     Solve for x:   

[Solution]

  Solve for x: 

Solve

Step

Check 

Subtract 5 to both sides.

If x  = -1, then

If x  = -23/9, then

Square both sides to undo the square root.

9x2 + 30x + 25 = 2 –  2x

 Remember to use FOIL

9x2 + 30x + 25 = 2 –  2x

 Set equal to 0.Add –  2x
Subtract 2

9x2 + 32x + 23 = 0

(x + 1)(9x + 23) = 0

It factors!

x + 1 = 0 or 9x + 23 = 0 

Set each factor to zero

x = -1 or x = -23/9

Click Solving Linear Equations for help.

x = -1 is the only solution

Done!!
Always check the answers to make sure they work.  They may not work.

     Solve for x:     

[Solution]

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joe mcdonald

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Last Update 09.24.2010