can you change this equation into a formula?

Question

i need help, if I have, Ax squared, +Bx squared + c = 0,
can you change it into this formula, X= -B +- the square root of b squared minus A multiplied by C and all over 2a?and what are the steps,

Answer 1

first of all, ax^2 + bx + c = 0

ax^2 + bx = -c

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

Then, by using the "completing the square" method.....

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

a(x+(b/2a))^2 - (ab^2/4a^2) = -c remember to multiply "a"

to "-(b/2a)^2" !!

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

Move "a" to right hand side.
(x+(b/2a))^2 = (b^2-4ac)/4a^2

Therefore, when you remove the squares of the equation, you get :

x + (b/2a) = +/-(sq root)(b^2-4ac)/2a

Hence

x = -b +/- (sq root)(b^2-4ac) / 2a

Q.E.D

Answer 2

Ax squared + Bx squared + c = 0

I will try to interpret that into (using ^ as power notation):

a x^2 + b x^2 + c = 0
<=> (a+b)x^2 + c = 0
<=> (a+b)x^2 = -c
<=> x^2 = -c / (a+b)
<=> x = + sqrt(-c / (a+b)),
x = - sqrt(-c / (a+b))

where sqrt (z) = square root of z

The last equation looks nothing like what you described as the formula you want, perhaps you are not expressing the first equation right?

Answer 3

Quadratic equation

ax² + bx² + c = 0

The degree of the polynomial equation is the highest term in the equation (ax²) or x squared or x th the second power, x² named qjuadratic equation,

a, b, and c are real numbers. the x are variables

- - - - - - -s-

Answer 4

I'm assuming you mistyped the equation, but if not.
Ax^2 + Bx^2 + C = 0
(A + B)x^2 + C = 0
x^2 = -C / (A + B)
x = +-sqrt{-C / (A + B)}

Now if you did mistype, you also mistyped the quadratic formula too.

Ax^2 + Bx + C = 0
A(x^2 + B/A x) + C = 0
A(x^2 + B/A x + B^2/4A^2 - B^2/4A^2) + C = 0
A(x + B/A x + B^2/4A^2) - B^2/4A + C = 0
A(x + B/2A)^2 = B^2/4A - C
A(x + B/2A)^2 = (B^2 - 4AC)/4A
(x + B/2A)^2 = (B^2 - 4AC)/4A^2
x + B/2A = +-sqrt{(B^2 - 4AC)/4A^2}
x + B/2A = +-sqrt{B^2 - 4AC}/2A
x = -B/2A +-sqrt{B^2 - 4AC}/2A
x = [-B +-sqrt{B^2 - 4AC}] / 2A