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