in the given equation, $c$ is a constant. if the equation has exactly one solution, what is the value of…

in the given equation, $c$ is a constant. if the equation has exactly one solution, what is the value of $c$?\nenter your numerical answer\nenter your answer...\nenter your answer as a number, fraction, or decimal

in the given equation, $c$ is a constant. if the equation has exactly one solution, what is the value of $c$?\nenter your numerical answer\nenter your answer...\nenter your answer as a number, fraction, or decimal

Answer

Explanation:

Step1: Clear the fractions

Multiply through by (72cx) to get (72 = x^{2}c+72x). Rearrange to (cx^{2}+72x - 72=0).

Step2: Use the discriminant formula

For a quadratic equation (ax^{2}+bx + c = 0) (here (a = c), (b = 72), (c=-72)), the discriminant (\Delta=b^{2}-4ac). Since the equation has exactly one solution, (\Delta = 0). So, (\Delta=(72)^{2}-4\times c\times(-72)=0).

Step3: Solve for (c)

Expand the equation: (5184 + 288c=0). Subtract 5184 from both sides: (288c=-5184). Then (c=\frac{-5184}{288}=- 18).

Answer:

(-18)