Lisa is using the equation x2 (x - 5) 2 = 157 to find two numbers that differ by 5 and that have squares that sum to 157. when lisa solves the problem using the zero product property, what do the two solutions represent?

X² + (x - 5) ² = 157

x² + x² - 10 x + 25 = 157

2 x² - 10 x - 132 = 0

2 (x² - 5 x - 66) = 0

2 (x² - 11 x + 6 x - 66) = 0

2 (x (x - 11) + 6 (x - 11)) = 0

2 (x - 11) (x + 6) = 0 (The zero-product property)

x - 11 = 0, x = 11

x + 6 = 0, x = - 6

There are two solutions:

1. Two numbers that differ by 5 and have squares that sum to 157 are 11 and 6 (6 = 11-5, 11² + 6² = 121 + 36 = 157)

2. Same is for the numbers - 6 and - 11

( - 11 = - 6 - 5, (-6) ² + (-11) ² = 36 + 121 = 157)