Final Answer:
The value of x in the given equation 251x = 100 in base two is equal to 011111101.
Step-by-step explanation:
To solve the given quadratic equation 251x = 100 in base two, we start by converting the given equation into the binary form i.e. 11111101x = 1100100. Now, to solve the equation, we will need to divide both sides of the equation by the coefficient of x i.e. 11111101. When we divide both sides of the equation by 11111101, we get x = 1100100/11111101. By further simplifying, we get x = 011111101. Thus, the value of x in the given equation 251x = 100 in base two is equal to 011111101.
The above method of solving the equation is a simple and straightforward method. However, we can also solve this equation by first converting the equation into its decimal form and then converting the answer back into the binary form.
To convert the equation into its decimal form, we need to multiply both sides of the equation by 251. This gives us, 251x x 251 = 100 x 251. After simplifying, we get x = 400/251. This is our answer in decimal form. To convert this answer back into the binary form, we need to use the binary conversion table. By looking at the table, we can see that 400/251 in binary form is equal to 011111101. Thus, this method also gives us the same answer i.e. 011111101.