Question

3x²+4x+1=0
using completing the square method​

Answer 1

`x= (-1)/(3)` or
`x= -1`

Explanation:

Step 1: Subtract 1 from both sides. 3x2+4x+1−1=0−1 3x2+4x=−1

Step 2: Since the coefficient of 3x^2 is 3, divide both sides by 3. 3x2+4x 3 = −1/3 x2+ 4/3 x= −1/3

Step 3: The coefficient of 4/3x is 4/3. Let b=4/3. Then we need to add (b/2)^2=4/9 to both sides to complete the square.

Add 4/9 to both sides. x^2+ 4/3 x+ 4/9 = −1/3 + 4/9 x^2+ 4/3 x+ 4/9 = 1/9

Step 4: Factor left side. (x+ 2/3 )^2= 1/9

Step 5: Take square root. x+ 2/3 =±√ 1/9 Step 6: Add (-2)/3 to both sides. x+ 2/3 + −2/3 = −2/3 ±√ 1/9 x= −2/3 ±√ 1/9 x= −1/3 or x=−1