Question

Solve the following quadratic equation by completing the square method

${\displaystyle \frac{5x+7}{x-1}}$ = 3x + 2

Answer 1

(3x + 2) (x – 1) = 5x + 7

3x² – 3x + 2x – 2 = 5x + 7

⇒ 3x² – x – 5x – 2 – 7 = 0

3x² – 6x – 9 = 0

⇒ x² – 2x – 3 = 0 ....(divided by 3)

x² – 2x = 3

Adding ${\displaystyle {(\frac{1}{2}\times 2)}^2}$ on both sides

x² – 2x + 1 = 3 + 1

(x – 1)² = 4

⇒ x – 1 = ${\displaystyle \sqrt{4}}$

x – 1 = ± 2

x – 1 = 2 or x – 1 = – 2

x = 3 or x = – 1

The solution set is – 1 and 3