quadratic equations?

Question

Math teacher gave us a project, but I have no idea how to do it, can u explain it, or show me how to do it?

"applying the "compeating the square" method to the equation given above, show that it's roots (values of x) are expressed by the quadratic formula:

equation given above- a(x squared) + bx +c = 0

Answer 1

ax^2 + bx + c = 0
ax^2 + bx = -c .... then divide by a

x^2 + (b/a) x = -c/a

to complete the square of the left side... divide the linear coefficient by 2 and square... that will be the constant ...

thus
x^2 + (b/a)x + b^2/4a^2 = -c/a + b^2/4a^2

(x + b/2a)^2 = [-4ac + b^2] / 4a^2

now... extract the square root... there will be a "±" on the right side...
and finally transpose b/2a

you now have the quadratic formula for x.


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Answer 2

ax² + bx +c = 0

Solve by completing the square

Divide thru by a

x² + (b/a)x + c/a = 0

Divide (b/a) by 2 and square, is (1/4)(b²/a²)
and add to both sides

x² + (b/a)x + (1/4)(b²/a²) + c/a = (1/4)(b²/a²)

Subtract c/a from both sides

x² + (b/a)x + (1/4)(b²/a²) = (1/4)(b²/a²) - c/a

Now on the left side you have a perfect square

(x + b/(2a))² = (b² - 4ac)/4a²

take the square root of both sides

(x + b/(2a)) = ±√(b² - 4ac)/2a

subtract b/(2a) from both sides

x = (-b ± √(b² - 4ac))/2a

This is the quadratic formula.
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Answer 3

I can show you how it applies. It involves the derivation of the formula, which I can show you by scanning it and sending it to you on Monday. If you could send me an email at [e-mail] that would be good.