The sum of the squares of two consecutive numbers is 145. Find them.

Sure, let's solve this step by step.

Step 1: Let's denote the two consecutive numbers as x and x+1.

Step 2: According to the problem, the sum of the squares of these two numbers is 145. So, we can write the equation as:

x^2 + (x+1)^2 = 145

Step 3: Simplify the equation:

x^2 + x^2 + 2x + 1 = 145

Step 4: Combine like terms:

2x^2 + 2x + 1 - 145 = 0

Step 5: Simplify the equation:

2x^2 + 2x - 144 = 0

Step 6: Divide the equation by 2 to simplify:

x^2 + x - 72 = 0

Step 7: Factor the equation:

(x - 8)(x + 9) = 0

Step 8: Set each factor equal to zero and solve for x:

x - 8 = 0 or x + 9 = 0

So, x = 8 or x = -9

Therefore, the two pairs of consecutive numbers that satisfy the equation are 8 and 9 or -9 and -8.