Question

Solve by using the quadratic formula X²-4x-4=0

Answer 1

4.82842712474619
-0.8284271247461903

go to google and type in quadratic equation solver it does it for you

Answer 2

\[\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]

Answer 3

a is the first coefficient; b is the second coeff, and c is the third coeff.

ax^2 + bx + c

Answer 4

Just plug into the formula Amistre gave you, OR go to Khan Academy if you want to see how it is derived. Fascinating process! Convinced me of its verity as well.

Answer 5

completing the square is a fun way to derive it :)

Answer 6

but that involves learning what it means to "complete" a square ..

Answer 7

x^2 -4x would be constructed like this:

\begin{array}c
1&2&-x\\
3&4&-x\\
-x&-x&x^2
\end{array}

to complete the square we need to ADD 4 to our equation

x^2 -4x +4 represents a "complete" square now.

But, we cant just go adding stuff to equations, that throws everything out of whack.

if we add 4 we also have to subtract 4; in other words, add a useful form of 0 so that value remains unchanged.


(x^2 -4x +4) -4 -4 = 0

the completed square can be compacted to this:

(x-2)^2 - 8 = 0, which transforms to (x-2)^2 = 8

+-sqrt(8) is what we need; so get rid of that -2 by adding 2 into it;

x = 2 +- sqrt(8)

x = 2 +- 2sqrt(2)

either route you take you still have to "complete" the square :)