ax+b/cx+d=2
solve for x
As written, you have
ax + b/cx + d = 2
acx^2 + (d-2)cx + b = 0
x = [c(2-d)±√((c(d-2))^2-4abc)]/2ac
I assume you meant
(ax+b)/(cx+d)=2
2(ax+b) = (cx+d)
2ax + 2b = cx + d
(2a-c)x = d-2b
x = (d-2b)/(2a-c)
To solve for x in the equation ax + b/cx + d = 2, we need to isolate the variable x.
Step 1: Start by multiplying both sides of the equation by the common denominator of cx and c.
cx(ax + b/cx + d) = 2c
Simplifying the left side of the equation gives:
acx^2 + bc + cdx = 2c
Step 2: Bring all terms to one side of the equation to create a quadratic equation.
acx^2 + cdx - 2c + bc = 0
Step 3: Factor out the common factor of c from the equation.
c(ax^2 + dx - 2 + b/c) = 0
Step 4: Set each factor equal to zero and solve for x.
1) cx = 0 => x = 0
2) ax^2 + dx - 2 + b/c = 0
Now, to solve the quadratic equation, you can use various methods such as factoring, completing the square, or using the quadratic formula.
However, since the equation given may not always be easily factorable or reducible, let's solve it using the quadratic formula:
x = (-d ± √(d^2 - 4ac))/(2a)
So, plugging in the values from the equation ax^2 + dx - 2 + b/c = 0, we have:
x = (-d ± √(d^2 - 4ac))/(2a)
x = (-d ± √(d^2 - 4ac))/(2a)
Therefore, the solution for x in the equation ax + b/cx + d = 2 is x = 0 or x = (-d ± √(d^2 - 4ac))/(2a).