[20]factorization 文字題

Assume that the square in the figure is the flower-bed.

By Pythagorean theorem, Length of each side of the square
= Hypotenuse of each right-angled triangle
= √[x² + (x + 1)²]

{√[x² + (x + 1)²]}² = 5
x² + (x + 1)² = 5
x² + x² + 2x + 1 = 5
2x² + 2x - 4 = 0
x² + x - 2 = 0
(x + 2)(x - 1) = 0
x = -2 (rejected) or x = 1