Factor, complete the square, use the quadratic formula, and use a graph to find the zeros of following equation: 15x^2-4x-68=0

Quadratic Formula:    For this equation   a = 15  b = -4  and  c = -68

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

 

x = (4 +- sqrt(16-(-4080) ) /   30

 = (4+-64)  /30     =   2.2667    or    -2

 

 

Complete the square

 

15x^2-4x-68    = 0     divide by 15

x^2 - 4/15x  - 4.5333... = 0

x^2 - 4/15x     = 4.53333....     now take 1/2 of the 'x' coefficient, square that and add it to both sides

x^2 - 4/15x + 4/225 = 4.53333... + 4/225   and this equals:

(x-2/15) ^2   =  4.55111     Now take the square root of both sides

x-2/15   =  +-  2.1333        so x=

x=    2/15 +-2.13333   =  2.2667      - 1.999999 (~ - 2)      Same answers as above

 

Factoring ...ya just gotta practice at these

(15x -34)(x+2) = 0         results in x = -2  or  34/15 = 2.2667    Same answers as above

 

 

I'm not sure how to put a graph in this answer, but if you graph the original equation, you will see a parabola that crosses the x-axis at -2 and 2.2667      (this web calc can graph it for you