Solve x2=2564%0D%0A%0D%0A2%0D%0A=%0D%0A25%0D%0A64%0D%0A by inspection. There are two real solutions. Enter the lesser number first. Leave the answers in simplest fraction form.

Answer 1

To solve the equation x^2 = 2564%, we can start by simplifying 2564% to a decimal. 2564% is equivalent to 2564/100 = 25.64 as a decimal.

Now the equation becomes x^2 = 25.64.

To find the real solutions, we can take the square root of both sides of the equation. However, it's important to note that the square root of a number can have both a positive and a negative value.

So, taking the square root of both sides:

√(x^2) = √25.64

x = ± √25.64

Simplifying the square root:

x = ± 5.064

The two real solutions are x = -5.064 and x = 5.064.

Now let's solve the second equation 2 = 25/64.
To write it in simplest fraction form, we just need to flip the fraction and simplify:

2 = 25/64

2 = (25/64) * (64/64) (multiplying by 1 to keep the value unchanged)

2 = 1600/64

2 = 800/32

2 = 25/8

So the second equation simplifies to 2 = 25/8.

Therefore, the solutions to the given equations are:
x = -5.064
2 = 25/8