Question 336454
how do you use the quadratic formula?
<pre><b>
You first get the equation in this form with the {{{red(A)}}} positive:

{{{red(A)x^2 + blue(B)x + green(C) = 0}}}

then you substitute in this

{{{x = (-blue(B) +- sqrt(blue(B)^2-4*red(A)*green(C) ))/(2*red(A)) }}} 

Then you simplify and you get two answers, one using the + and
one using the -.

Example:

{{{-blue(9)x -red(3)x^2 = green(2)}}}

Write it in descending order on the left with only 0 on the right:

{{{-red(3)x^2 - blue(9)x - green(2) = 0}}}

Multiply through by -1 to make the first term {{{red(A)}}} positive:

{{{red(3)x^2 + blue(9)x + green(2) = 0}}}

{{{x = (-blue(9) +- sqrt(blue(9)^2-4*red(3)*green(2) ))/(2*red(3)) }}}

Now simplify:

{{{x = (-9 +- sqrt(9^2-4*3*2) )/6 }}}

{{{x = (-9 +- sqrt(81-24) )/6 }}}

{{{x = (-9 +- sqrt(57) )/6 }}}

The two solutions are:

{{{x = (-9 + sqrt(57) )/6 }}} and {{{x = (-9 - sqrt(57) )/6 }}}

You can get the approximate decimal values with a calculator:

{{{x = -.2416942608 }}}  and {{{x = -2.758305739 }}}

Edwin</pre>