We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
57
2
avatar

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

 Jun 25, 2019
 #1
avatar+8406 
+2

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+101813 
+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

3 Online Users