-14x2+44x-6=0

Question

Algebra problem

Answer 1

-14x²+44x-6=0

14x²-44x+6=0

2(7x²-22x+3)=0

7x²-22x+3=0

(7x-1)(x-3)=0

7x-1=0

7x=1

x=1/7

x-3=0

x=3

Answer 2

If the problem asks to solve for x, you can also directly use the quadratic formula (derived from completing the square).

Answer 3

Factor out -14 :

      -14(x² - 44/14 x + 6/14) = 0

 

divide both sides by -14

     (x² - 44/14 x + 6/14) = 0

 

simplify the terms

     (x² - 22/7 x + 3/7) = 0

 

solve by completing the square. Move the 3/7 term to the right side of the equation

     x² - 22/7 x = -3/7

 

Take half if the term with x : -22/7   and square it:   (-11/7)² = 121/49

now add 121/49 to both sides:

 

      x² - 22/7x + 121/49 = 121/49 - 3/7

 

Simplify the right side

      x² - 22/7x + 121/49 = 100/49

 

write the expression on the left as a square

 

      (x - 11/7)² = 100/49

 

and take the square root of both sides

      x - 11/7 = 10/7        positive root

      x - 11/7 = -10/7       negative root

 

solve for x

      x = 10/7 + 11/7 = 21/7 = 3     or

      x = -10/7 + 11/7 = 1/7

 

so the two possible solutions are x = 3 or x = 1/7.

Plug these numbers back into the original equation to verify the answers.