Solve (question no. 2-22) for x :

(x - 5)² - (x + 2)² = -2

(x - 5)² - (x + 2)² = -2

Using the formula,

[∵ (x - y)² = x² + y² - 2xy]

And,

[∵ (x + y)² = x² + y² + 2xy]

⇒ x² + 5² - 2 $\times$ x $\times$ 5 - (x² + 2² + 2 $\times$ x $\times$ 2) = -2

⇒ x² + 25 - 10x - (x² + 4 + 4x) = -2

⇒ x² + 25 - 10x - x² - 4 - 4x = -2

⇒ 21 - 14x = -2

⇒ - 14x = -2 - 21

⇒ - 14x = - 23

⇒ x = $\dfrac{23}{14}$

⇒ x = $1\dfrac{9}{14}$

Hence, the value of x is $1\dfrac{9}{14}$.