quadradic equation vs quadratic formula

[drt_t1gg3r]

quadratic equation
ax[sup:1l3u07s6]2[/sup:1l3u07s6] + bx + c = 0

divide both sides by a
x[sup:1l3u07s6]2[/sup:1l3u07s6] + b/a +c/a(x) = 0/a

subtract c/a from both sides
x[sup:1l3u07s6]2[/sup:1l3u07s6] + b/a(x) = - c/a

complete the square and add the completion to both sides (I have a basic understanding of completing the squares but could someone explain more than dividing the b component in half then squaring it?)
x[sup:1l3u07s6]2[/sup:1l3u07s6] + b/a(x) +(b/2a)[sup:1l3u07s6]2[/sup:1l3u07s6] = (b/2a)[sup:1l3u07s6]2[/sup:1l3u07s6] - c/a

factor left side
(x + b/2a)[sup:1l3u07s6]2[/sup:1l3u07s6] = (b/2a)[sup:1l3u07s6]2[/sup:1l3u07s6] - c/a

find common denominator for right side
(x + b/2a)[sup:1l3u07s6]2[/sup:1l3u07s6] = b[sup:1l3u07s6]2[/sup:1l3u07s6]/4a[sup:1l3u07s6]2[/sup:1l3u07s6] - c/a
(x + b/2a)[sup:1l3u07s6]2[/sup:1l3u07s6] = (b[sup:1l3u07s6]2[/sup:1l3u07s6] - 4ac)/4a[sup:1l3u07s6]2[/sup:1l3u07s6] <-----this is the part I don't understand? how is (b[sup:1l3u07s6]2[/sup:1l3u07s6] - 4ac)/4a[sup:1l3u07s6]2[/sup:1l3u07s6] the common denominator?

take the square of both sides
x + b/2a = + sqr((b[sup:1l3u07s6]2[/sup:1l3u07s6] - 4ac)/4a[sup:1l3u07s6]2[/sup:1l3u07s6]))

subtract b/2a from both sides
x = -b/2a + sqr((b[sup:1l3u07s6]2[/sup:1l3u07s6] - 4ac)/4a[sup:1l3u07s6]2[/sup:1l3u07s6]))
becomes the quadratic formula

 

[Denis]

quadratic equation
ax[sup:11ry0lfv]2[/sup:11ry0lfv] + bx + c = 0
divide both sides by a
x[sup:11ry0lfv]2[/sup:11ry0lfv] + b/a +c/a(x) = 0/a
subtract c/a from both sides
x[sup:11ry0lfv]2[/sup:11ry0lfv] + b/a(x) = - c/a

WHAT are you trying to do?

divide both sides by a: x^2 + bx/a +c/a = 0

subtract c/a from both sides: x^2 + bx/a = -c/a

 

[Loren]

\(\displaystyle b^2/4a^2 - c/a\)

\(\displaystyle \frac{b^2}{4a^2}-\frac{c}{a}\)

\(\displaystyle \frac{b^2}{4a^2}-\frac{c}{a}\cdot\frac{4a}{4a}\)

\(\displaystyle \frac{b^2}{4a^2}-\frac{4ac}{4a^2}\)

\(\displaystyle \frac{b^2-4ac}{4a^2}\)

 

[stapel]

complete the square and add the completion to both sides (I have a basic understanding of completing the squares but could someone explain more than dividing the b component in half then squaring it?)

Um... What "more" do you need? The "dividing in half and squaring" is what puts the variable-containing portion of the expression into "completed square" form. If you "understand" completing the square, then what don't you understand about... well, completing the square? :shock:

Please reply with clarification. Thank you!

Eliz.