Other Types of Equations 

-- Part 1.5 --

  Solve for x20x3 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

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 x2x3 + x2  2x 1 = 0

Solve

Step

Check 

2x3 + x2  2x 1 = 0

Use the grouping method
 

If x  = -, then
2(-
)3+(-)22(-)1=0
    2(-1/8)++11 = 0
- + = 0
0 = 0

If x  = 1, then
2(
1)3+(1)22(1)1 = 0
    2 + 1 2 1 = 0
0 = 0

If x  = -1, then
2(-
1)3+(-1)22(-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 xx3 + 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]

Send comments, suggestions or report errors to:
joe mcdonald

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Last Update 09.23.2010