If ax^2 + bx + c = 0 then what is x?

Question

Can some one please explain how to get the answer???

Answer 1

The process required is known as 'completing the square'.

Divide ax^2 + bx + c = 0 by a:
x^2 + (b/a)x + (c/a) = 0
Subtract c/a from each side:
x^2 + (b/a) x = -c/a
Add to each side the square of half the coefficient of x:
x^2 + (b/a)x + (b/2a)^2 = -c + (b/2a)^2
x^2 + (b/a)x + (b/2a)^2 = (b^2 - 4ac) / 4a^2
Factorise the LHS as a square:
(x + b/a)^2 = (b^2 - 4ac) / 4a^2
Take square roots:
x + b/a = +/- (b^2 - 4ac) / 2a
Subtract b/a:
x = ( -b +/- sqrt(b^2 - 4ac) ) / 2a.

Answer 2

First you should see if
a=0
then you get:
bx+c=0
then, if
b=0 you get c=0 and x from R
if b is not 0 then
x=-c/b
and then, if a is not 0 you can divide:

"Divide ax^2 + bx + c = 0 by a:
x^2 + (b/a)x + (c/a) = 0
Subtract c/a from each side:
x^2 + (b/a) x = -c/a
Add to each side the square of half the coefficient of x:
x^2 + (b/a)x + (b/2a)^2 = -c + (b/2a)^2
x^2 + (b/a)x + (b/2a)^2 = (b^2 - 4ac) / 4a^2
Factorise the LHS as a square:
(x + b/a)^2 = (b^2 - 4ac) / 4a^2
Take square roots:
x + b/a = +/- (b^2 - 4ac) / 2a
Subtract b/a:
x = ( -b +/- sqrt(b^2 - 4ac) ) / 2a."

Answer 3

x = {-b ± sqrt (b^2 - 4ac)} / 2a

This is the quadratic formula. You need to know your values of a, b and c to find this out. However, you can factorise the equation a lot of the time for much easier results.

For example:

3x^2 + 9x + 6 = 0
(3x + 3)(x+2) = 0

either 3x + 3 = 0 or x + 2 = 0

so 3x = -3, x = -1
OR x = -2


I factorised this by thinking what numbers multiplied together to give 6. My best guess was 3 and 2. I also thought what coefficients of x multiplied together to give 3x^2, I thought 3x and x. I then tried to get 9x by multiplying 3x and x by 3 and 2 in various forms, and adding them together to try and get 9x.
3x * 2 and x * 3 worked, so the brackets must be (3x + 3) and (x + 2).

Answer 4

ax^2 + bx + c = 0

2ax^ + c = - bx

Dividing by - b on both sides -

-2ax^ / b - c / b = bx / b ( - sign gets cancelled on the numtr and dentr)

-2ax^ / b - c / b = x

Therefore,

X = - 1 / b ( 2ax^ + c )

Answer 5

x = [- b ± √(b² - 4ac)] / 2a
Example
Solve 2x² + 7x + 6 = 0
a = 2
b = 7
c = 6
x = [- 7 ± √(7² - 4 x 2 x 6)] / 4
x = [- 7 ± √1] / 4
x = - 6/4 , x = - 8/4
x = - 3/2 , x = - 2
Hope this helps.

Answer 6

What you you get for x is also called the quadratic equation.