9xsquared + 4 = 2x solve using the quadratic fromula

Question

 9x²+4=2x   Solve using the quadratic formula. 

Answer 1

9x^2 + 4 = 2x                                              move the 2x

9x^2 -2x + 4 = 0    <=>  ax^2 +bx + c = 0    correct form

 

 a=9  b=-2  c=4                                            variables

 

(b +/- (b^2 -4ac)^(1/2))/2a                           equation

 

(-2 +/- ((-2)^2 -4(9)(4))^(1/2))/(2(9))         everything plugged in

 

(-2 +/- ( (4) -4(36))^(1/2))/18                     multiplying

 

(-2 +/- (4-144)^(1/2))/18                            more multiplying

 

(-2 +/- (-140)^(1/2))/18                              parentheses

 

(-2 +/- i(140)^(1/2))/18                               simplify the radical                (140)^(1/2) = (7*5*2*2)^(1/2) = 2(35)^(1/2)

 

(-2 +/- 2i(35)^(1/2))/18                              Simplify everything

 

(-1 +/- i(35)^(1/2))/9                                 split up equations

 

(-1 + i(35)^(1/2))/9  and  (-1 - i(35)^(1/2))/9     answers

 

 

Let me know if you have any questions.  Hope this helps

 

John

 

Answer 2

9x²  + 4 = 2x

        -2x=-2x

---------------------

9x² -2x + 4 = 0

 

a = 9; b = -2; c = 4

 

 

x = ( -b + sqrt(b² - 4ac) ) / 2a                              and                 x = ( -b - sqrt(b² - 4ac) ) / 2a

   = (-(-2) + sqrt( (-2)(-2) - 4(9)(4) ) / 2(9)                                       (Similar to the + solution shown on the left)

   = (2 + sqrt( 4 - 36(4) ) / 18

   = (2 + sqrt( 4 - 144 ) )  / 18

   = (2 + sqrt( -140 ) ) / 18

   = (2 + sqrt( -1(7)(4)(5) ) / 18

   = (2 + (i)(sqrt (4(35) ) / 18            sqrt(-1) = i

   = (2 + (i)(2)(sqrt(35)) / 18              sqrt(4) = 2

   = (2 + 2i(sqrt(35))  ) / 18                 

   = 2(1 + i(sqrt(35)) ) / 2(9)           Cancel 2/2 = 1

   = (1 + i(sqrt(35)) ) / 9 

 

Please let me know if you would like to set up a time to tutor further on this topic.

 

Thanks!

Susan