How would one write a proof for this?

Question

Given: 0=ax^2+bx+c
Prove: x=(-b±√(b^2-4ac))/(2a)

Basically, what individual steps would be taken to go from the quadratic equation to the quadratic formula.

This is not my homework.

Answer 1

The first thing you do is get you x's on one side,
Ax^2 + bx = -c
Then remove the coffient for the x2
x^2 + b/a x = -c/a
Complete the square
x^2 + b/a x + b^2/4a^2 = (b^2 - 4ac)/(4a^2), which equals
(x + b/2a) 2= (b^2 -4ac)/(4a^2), take the square root

x + b/2a = √((b^2 - 4ac)/(4a^2)) = √(b^2 -4ac)/2a
Subtract - (b/2a) from both sides and you have the answer
x=(-b±√(b^2-4ac))/(2a)
Looks like a mess with all the () but hope that helps.


x + b/2a = Sq rt. ((b^2 - 4ac)/(4a^2)) = sq.rt (b^2 -4ac)/2a
subtract - (b/2a) from both sides and you have the answer
x=(-b±√(b^2-4ac))/(2a)
Looks like a mess with all the () but hope that helps.

Answer 2

Complete the square.

0 =
ax^2+bx+c =
a(x^2 + (b/a)x + c/a) =
a[(x+b/(2a))^2 + c/a - b^2/(4a^2)].

Now, solve (x+b/(2a))^2 + c/a - b^2/(4a^2) = 0.

Rearrange:
(x+b/(2a))^2 = b^2/(4a^2) - c/a
Square root:
x+b/(2a) = +/-sqrt( b^2/(4a^2) - c/a )
Solve for x:

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

Answer 3

Do ur home work ur self
put value of x in first equation to solve this