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Solve for x: (3x + 12)(x + 4) = (4x^2 + 8x + 8x^2)/(2x).

 Jun 21, 2022
 #1
avatar+124524 
+1

(3x + 12) (x + 4)  =  (4x^2 + 8x  + 8x^2) / (2x)               assuming that  x   is not 0

 

3x^2  +24x + 48  =  (4x) ( x + 2 + 2x) / ( 2x)

 

3x^2 + 24x + 48  = 2 ( 3x + 2)

 

3x^2 + 24x + 48  = 6x  + 4

 

3x^2 + 18x + 44  = 0

 

Using the Q formula

 

              -18  ± √ (18^2  - 4 * 3 * 44)       -18  ± √ ( -204)         -18  ± 2√51 i

x =         ______________________   = ____________  =  ____________ =   -3  ± √51 i / 3

                         2 * 3                                        6                             6

 

 

cool cool cool

 Jun 21, 2022
 #2
avatar+2339 
+1

Simplify the equation to: \(3(x+4)(x+4) = 2x(6x + 4) \div 2x\)

 

Note the 2x's on the right-hand side cancel out, so we have: \(6x+4 = 3(x+4)(x+4)\)

 

Now, expand the right-hand side: \(6x+4 = 3x^2 + 24x + 48\)

 

Convert into a quadratic: \(0 = 3x^2 + 18x + 44\)

 

Now, use the quadratic formula, and \(x = \color{brown}\boxed{{-3 \pm \sqrt {51} \over 3}}\)

 Jun 21, 2022

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