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Solve each equation

 Feb 22, 2019
edited by GAMEMASTERX40  Feb 22, 2019
edited by GAMEMASTERX40  Feb 22, 2019
 #1
avatar+19686 
0

-x^2 + 4x = 13      re-arrange

-x^2+4x-13 = 0     easier to work with if you multiply both sides by -1

x^2-4x+13 = 0      Use quadratic Formula   a = 1    b = -4    c = 13

 

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)      results in      [4+-sqrt(16-4(1)13) ] / 2    =   2 +- sqrt(-36)/2   =   2 +- sqrt 3i

 Feb 22, 2019
 #2
avatar+5 
-4

Sorry...I posted the wrong math problem...again.

GAMEMASTERX40  Feb 22, 2019
 #3
avatar+104627 
+4

10

 

-3 + √[10x + 9 ] = x         the idea is to get the radical on one side and everything else on the other

 

Also....these problems sometimes produce extraneous solutions....we need to be aware of that

 

Add 3 to both sides

 

√[10x + 9 ]  = x + 3       square both sides

 

10x + 9  =  x^2 + 6x + 9    

 

10x = x^2 + 6x

 

x^2 - 4x  = 0

 

x ( x - 4) = 0

 

x = 0     or   x = 4

 

Check that both of these solutions are good !!!

 

 

cool cool cool

 Feb 22, 2019
 #4
avatar+104627 
+3

b)   Divide both sides by 2   to make the numbers smaller

 

√ [ 44 - 2x ]  =   x - 10          square both sides

 

44 - 2x  =    x^2 - 20x + 100     rearrange as

 

x^2 - 18x + 56 =  0      factor as

 

(x - 14) ( x - 4) =  0

 

Set both factors to 0 and solve for x and we get that

 

x = 14     or  x  = 4

 

The first solution is good, GM

 

The second isn't because it makes the right side of the original equation negative.......but we cannot get a negative result from a positive radical....!!!!

 

 

cool cool cool

 Feb 22, 2019
 #5
avatar+104627 
+3

Last one...square both sides straight away  and we get that

 

x^2 - 8x + 16 = 2x     rearrange as

 

x^2 - 10x + 16  = 0    factor

 

(x - 8) ( x - 2)  = 0

 

x = 8      or  x = 2

 

Note that 8 does not work   because 8 - 4   does not equal     - √ (2 * 8)  =  - √16   =  - 

 

Note that   x = 2 is good

 

2 - 4  = - √(2 * 2)

 

-2  = -√4

 

-2 = - 2   !!!

 

 

cool cool cool

 Feb 22, 2019

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