Solve the following quadratic equations by factorization: (x - 5)(x - 6) = 25/(24)^2

Question

Solve the following quadratic equations by factorization:

\((x - 5)(x- 6) =\frac{25}{(24)^{2}}\)

Answer 1

In factorization, we write the middle term of the quadratic equation either as a sum of two numbers or difference of two numbers such that the equation can be factorized.

\((x - 5)(x-6)=\frac{25}{(24)^{2}}\)

⇒ x² – 11x + 30 = 25/(24)² 

⇒ x² – 11x + 121/4 – 121/4 + 30 = 25/(24)² 

⇒ x² – 11x + 121/4 = 25/(24)² + 1/4 

⇒ x² – 11x + 121/4 = 676/(4 × 24²) 

⇒ (x – 11/2)² = (13/24)²