Question

What is the value of x in the equation 44° = 18x - 3 / (6 + 25x)?

a) 2
b) 3
c) 4
d) 5

Answer 1

To find the value of x in the equation 44° = 18x - 3 / (6 + 25x), solve the quadratic equation 150x² + 282x - 264 = 0 using the quadratic formula. The two possible solutions for x are -0.42 and 1.76, but since the answer choices are integers, the value of x closest to the calculated values is 2 (option a).

Step-by-step explanation:

To find the value of x in the equation 44° = 18x - 3 / (6 + 25x), we need to solve for x. First, let's simplify the equation:

44 = 18x - 3 / (6 + 25x)

Multiply both sides of the equation by (6 + 25x) to eliminate the fraction:

44(6 + 25x) = (18x - 3)(6 + 25x)

Simplify the equation and move all terms to one side to get a quadratic equation:

150x² + 282x - 264 = 0

Now we can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values of a, b, and c from the quadratic equation, we get:

x = (-282 ± √(282² - 4(150)(-264))) / (2(150))

After simplifying, we find two possible values for x:

x ≈ -0.42 or x ≈ 1.76

Since answer choices are given as integers, the value of x closest to the calculated values is 2 (option a).