SOLUTION: in the formula shown here: http://www.algebra.com/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+d+%29%29%2F2a&x=0003 (paste in the browser) (note: this is the quadr

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: in the formula shown here: http://www.algebra.com/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+d+%29%29%2F2a&x=0003 (paste in the browser) (note: this is the quadr      Log On


   



Question 597910: in the formula shown here:
http://www.algebra.com/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+d+%29%29%2F2a&x=0003
(paste in the browser)
(note: this is the quadratic formula)
I do not understand what the little box means in the equation. (in between the 2 and a.) Please explain! and it will also help to explain the whole thing, as I don't really understand all the signs, as I haven't learnt any of it before...thanks in advance:)

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Depending on how much you've learned of algebra so far, this could be a little confusing or very confusing, but here it goes.

THE SYMBOLS FOR MULTIPLICATION:
At the bottom of the formula, between the 2 and the a , there is symbol called a middle dot.
That is a symbol used in algebra to mean multiplied by. The expression 2%2Aa means 2 times a.
In algebra, the letter x is used a lot. The old X multiplication sign that is used in third grade looks too much like the letter x. That old X symbol could cause confusion, so it is not used.
Sometimes a middle dot is used to indicate multiplication, as in
3%2A5=15 or 2%2Aa.
If there is no room for confusion, the middle dot can be skipped, so we are allowed to write 2a instead of 2%2Aa.
To make matters a little more confusing, the asterisk is used as a middle dot when typing a middle dot symbol is difficult or impossible. So you may see 2*a instead of 2a or 2%2Aa.

THE QUADRATIC FORMULA:
The quadratic formula is used to find solutions to quadratic equations like
15x%5E2-14x-8=0.
All quadratic equations can be represented with the general equation
ax%5E2%2Bbx%2Bc=0 where a, b, and c represent the numbers in the equation.
For 15x%5E2-14x-8=0, a is 15, b is -14, and c is -8.

Some quadratic equations have one or two real solutions. For other quadratic equations, there is no real number that could be a solution. It all depends on the value of an expression called the discriminant. In the formula you are asking about, the letter d represents the discriminant.

The discriminant is the expression
b%5E2-4ac The 4, a, and c are multiplied together.
For 15x%5E2-14x-8=0, the discriminant is
%28-14%29%5E2-4%2A15%2A%28-8%29=196%2B480=676
If the discriminant is positive (as for the equation 15x%5E2-14x-8=0, with d=676 for a discriminant), there are two distinct (meaning different) real solutions. They can be calculated using the formula
x=%28-b+%2B-+sqrt%28d%29%29%2F2a
For 15x%5E2-14x-8=0, it would be
x=%28-%28-14%29+%2B-+sqrt%28676%29%29%2F%282%2A15%29=%2814+%2B-+26%29%2F30
One solution is
x=%2814+%2B+26%29%2F30=40%2F30=4%2F3.
The other is
x=%2814+-+26%29%2F30=-12%2F30=-2%2F5.