solve the equation 9x2 -15x+6=0 by the method of completing the square
Answers
ax-by+c=0
1. Divide all terms by a so that a=1
2. Take c to the other side
3. Add (b/2)^2 to both the sides. (Be careful about the sign of 'b' and also do not forget to remove 'bx'.)
4. Remove the square from both sides
5. Now simplify to find x.
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Answer:
Step-by-step explanation:
Solution :-
Here, we have
⇒ 9x² - 15x + 6 = 0
Dividing equation by 9
⇒ x² - 15/9x + 6/9 = 0
⇒ x² - 5/3x + 2/3 = 0
Shifting constant term on RHS
⇒ x² - 5/3x = - 2/3
Adding square of half of coefficient of x on both sides
⇒ x² - 2(5/6)x + (5/6)² = (5/6)² - 2/3
⇒ (x - 5/6)² = 25/36 - 2/3
⇒ (x - 5/6)² = 25 - 24/36
⇒ (x - 5/6)² = 1/36
Taking square root of both sides
⇒ x - 5/6 = ± 1/6
⇒ x = 5/6 ± 1/6
⇒ x = 5/6 + 1/6 = 1 or 5/6 - 1/6 = 4/6 = 2/3
⇒ x = 1, 2/3
Hence, the roots of the equation are 1 and 2/3.