Quadratic formula?

Question

I need to know how to transform from ax^2 + bx + c = 0 to the quadratic formula.

Answer 1

Look at this site it with help you with all calculations

http://www.1728.com/quadratc.htm

Answer 2

First step as with "normal" quadratic equations, you'd get rid of the coeffiecient before the x^2 term, i.e. divide everything by a:

x^2 + (b/a)*x + c/a = 0 (this is ok since 0/a = 0)
Move the c/a to the right to complete the square:

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

To complete the square, you have to have the "middle term" in the form of 2xy (this stems from the factorization of a perfect square trinomial [(x + y)^2 = x^2 + 2xy + y^2]):

If 2xy = (b/a)*x, then y would = (b/2a)

To accomplish this, add the square of (b/2a) to both sides, giving (legal since you're doing it to both sides):

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

Using completing the square (x^2 + 2xy + y^2 = (x + y)^2), then the left side becomes:
(x + b/2a)^2 = -c/a + (b^2 / 4a^2) and we can rewrite the right side using common denominator as:

(x + b/2a)^2 = (-4ac +b^2) / 4a^2
rewrite the right again to look like the form we know:
(x + b/2a)^2 = (b^2 - 4ac) / 4a^2

If we take the sqare root of both sides, we get:

x + (b/2a) = ± sqrt(b^2 - 4ac) / 2a
the ± is because a square root (non-principal square root can be + or - like sqrt(16) = ±4)

Now subtract the b/2a from both sides:

x = (-b ± sqrt(b^2 - 4ac))/2a

Answer 3

the quadratic formula is used to solve the possible variable solutions in quadratic equations, which are equations in which the a variable is squared. the formula itself is: x = -b (+/-) (square root of (b^2-4ac) / 2a so given 2x^2 +9x + 4 a= 2 b= 9 c= 4 so then plugging it into the equation: x= (-9) (+/-) square root (9^2-4(2) (4) / 2(2) simplified: x= -9 (+/-) square root (49) / 4 x= (-9 + 7)/ 4 or (-9 - 7) /4 solved: x = -1/2, or -4 hope that helps! good luck...

Answer 4

You entered a=a, b=b, c=c,meaning you must want to solve the quadratic equation:


ax2bxc=0

Since a=0, this is not a quadratic equation, and the quadratic formula cannot be used to solve it.

Answer 5

The Quadratic formula is x=(-b±√(b^2-4ac))/(2a)

A can't = 0

Answer 6

ax^2 + bx + c = 0
Divide through by a:
x^2 +(b/a)x + c/a = 0
Complete the square:
x^ + (b/a)x +(b/2a)^2 -(b/2a)^2 + c/a = 0
Move "extra" terms to the right-hand side:
x^ + (b/a)x +(b/2a)^2 = (b/2a)^2 - c/a
Factor the left-hand side:
(x+(b/2a))^2 = b^2/4a^2 - c/a
Make the riht-hand side into a single fraction:
(x+(b/2a))^2 = (b^2 - 4ac)/4a^2
Take the square root of both sides:
x + b/2a = (±sqrt(b^2 - 4ac))/2a
Subtract b/2a from both sides
x = -b/2a + (±sqrt(b^2 - 4ac))/2a
convert to a single fraction again:
x = (-b ± sqrt(b^2 - 4ac)) / 2a

Answer 7

-B plus or minus the Square root (B^2 - 4AC)
all divided by 2A

Answer 8

the quadratic formula is x = [-b+Sqr(b^2-4ac)]/2a
and = [-b-sqr(b^d2-4ac)]/2a

Answer 9

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

Answer 10

x = ( -b ± √(b² - 4ac) ) / 2a