3x^2 + 6x = 12
To use the quadratic formula, we first have to set the quadratic equal to zero.
To do this, let's subtract color(red)(12) from both sides of the equation:
3x^2 + 6x quadcolor(red)(-quad12) = 12 quadcolor(red)(-quad12)
3x^2 + 6x - 12 = 0
Now, the equation is in standard form, or color(red)(a)x^2 + color(magenta)(b)x + color(blue)(c), so:
color(red)(a = 3), color(magenta)(b = 6), and color(blue)(c = -12)
The quadratic formula can solve for x in any case, and we use it especially when the expression is not factorable.
The quadratic formula is:
x = (color(magenta)(-b) +- sqrt(color(magenta)(b)^2 - 4color(red)(a)color(blue)(c)))/(2color(red)(a))
Now we can plug in our values for a, b, and c:
x = (color(magenta)(-6) +- sqrt((color(magenta)(-6))^2 - 4(color(red)(3))(color(blue)(-12))))/(2(color(red)(3)))
Simplify:
x = (-6 +- sqrt(36 - 4(-36)))/6
x = (-6 +- sqrt(36 + 144))/6
x = (-6 +- sqrt(180))/6
x = (-6 +- 6sqrt(5))/6
Divide by the denominator to get the simplified answer:
x = -1 +- sqrt5
Hope this helps!
