Final answer:
To solve the given equation 4/(w-4) = -(7)/(5w-20)+2, we can simplify both sides of the equation, eliminate the fractions, and solve the resulting quadratic equation. However, after solving, we find that there are no real solutions to the equation.
Step-by-step explanation:
To solve the equation 4/(w-4) = -(7)/(5w-20)+2, we can start by simplifying both sides of the equation.
First, let's simplify the right side of the equation:
-7/(5w-20) + 2 = [(-7)(5w-20)]/(5w-20) + 2 = (-35w+140)/(5w-20) + 2
Now, let's rewrite the equation:
4/(w-4) = (-35w+140)/(5w-20) + 2
To eliminate the fractions, we can multiply both sides of the equation by the least common denominator, which is (w-4)(5w-20). This will give us a quadratic equation to solve.
Multiplying both sides by (w-4)(5w-20), we get:
4(5w-20) = (-35w+140)(w-4) + 2(w-4)(5w-20)
Simplifying both sides, we get:
20w - 80 = -35w^2 + 140w + 140w - 560 + 10w^2 - 40w
Combining like terms, we have:
10w^2 + 20w - 80 = -35w^2 + 140w - 560 + 10w^2 - 40w
Setting the equation equal to zero:
45w^2 - 100w + 360 = 0
Now, we can use the quadratic formula to solve for w. The quadratic formula is:
w = (-b ± √(b^2 - 4ac))/(2a)
Plugging in the values from our quadratic equation:
w = (100 ± √((-100)^2 - 4(45)(360)))/(2(45))
Simplifying further, we get:
w = (100 ± √(10000 - 64800))/(90)
w = (100 ± √(-54800))/(90)
Since the square root of a negative number is not a real number, there are no real solutions to the equation.