Question

solve by completing square method 7x2=2x+6​

Answer 1

Correct Question :-

Solve by completing square method :

7x² = 2x + 6

Answer :-

x = (1 + √43)/7 or (1 - √43)/7

Explanation :-

Given, Equation :

7x² = 2x + 6

⇒ 7x² - 2x = 6

Divide throughout by 7

⇒ (7x²/7) - (2x/7) = 6/7

⇒ x² - (2x/7) = 6/7

It can be written as

⇒ (x)² - 2(x)(1/7) = 6/7

Adding (1/7)² on both the sides

⇒ (x)² - 2(x)(1/7) + (1/7)² = (6/7) + (1/7)²

⇒ (x - 1/7)² = (6/7) + (1²/7²)

[ ∵ a² - 2ab + b² = (a - b)² ]

⇒ (x - 1/7)² = (6/7) + (1/49)

⇒ (x - 1/7)² = (42 + 1)/49

⇒ (x - 1/7)² = 43/49

Taking square root on both the sides

⇒ √(x - 1/7)² = √(43/49)

⇒ x - 1/7 = ± √43/7

⇒ x = ± √43/7 + (1/7)

⇒ x = (1 ± √43)/7

⇒ x = (1 + √43)/7 or (1 - √43)/7

∴ x = (1 + √43)/7 or (1 - √43)/7

Answer 2

Answer:

Step-by-step explanation:

7x² = 2x + 6

x² = 2x/7 + 6/7

x² - 2x/7 - 6/7 = 0

x² - 2x/7 + (1/7)² - (1/7)² - 6/7 = 0

(x - 1/7)² - (1/49 + 6/7) = 0

(x - 1/7)² - (1 + 42)/49 = 0

(x - 1/7)² - (43)/49 = 0

(x - 1/7)² = 43/49

x  = ±(√43 / 7) + 1 / 7