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
