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The number $x$ satisfies $5x^2 + 4 = 3x + 9$. Find the value of $(10x - 3)^2$.

 Jun 25, 2019
 #1
avatar+8842 
+4

Note that   (10x - 3)2   =   (10x - 3)(10x - 3)   =   100x2 - 60x + 9

 

Now let's look at the given equation:

 

5x2 + 4  =  3x + 9

                                Subtract  3x  from both sides of the equation.

5x2 - 3x + 4  =  9

                                Subtract  4  from both sides of the equation.

5x2 - 3x  =  5

                                Multiply through by  20

100x2 - 60x  =  100

                                         Add  9  to both sides of the equation.

100x2 - 60x + 9   =   109

                                         And remember that  100x2 - 60x + 9  =  (10x - 3)2

(10x - 3)2   =   109

 Jun 26, 2019
 #2
avatar+106533 
+2

5x^2 + 4  = 3x + 9                  

5x^2 - 3x - 5  = 0       use the Quadratic Formula                  

 

3 ±√[ 109]

___________   =   x       which implies that

        10

 

10x  =  3 ±√109          subtract 3 from both sides

 

10x - 3  =  ±√109       square both sides

 

So

 

(10x - 3)^2  = ( ±√109)^2  =

 

109

 

 

 

cool cool cool

 Jun 26, 2019

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